Lojban Wave Lessons/Single page

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Made by la klaku with help from various Lojbanists. Based on the work of la .kribacr. Spring 2013.


These lessons are an attempt to expand on the Lessons originally started in Google Wave network, an excellent Lojban tutorial authored by la .kribacr., la xalbo, and transcribed by Marenz (which were parallel to lessons 1-4 of this tutorial). It explains newer rules of Lojban not covered by older materials such as "What is Lojban?" and "Lojban for Beginners".

If you are new to Lojban, I recommend listening to any recordings you can find of spoken Lojban (readings, music, conversation) both before and while you are taking this tutorial, in order to make yourself familiar with the sounds and words of the language. Furthermore, try to say the things you read in Lojban accent if it's reasonably practical. This can help your pronunciation a lot.

When taking this tutorial, it's best to pause between lessons in order to internalize what you have learnt. I have attempted to build these lessons from the bottom up and exclude any words or concepts that have not been explained in previous lessons. Once explained, they are used freely throughout the remainder of the tutorial. I urge readers not to pass any misunderstood content; if you have questions or are uncertain about something, feel free to ask the Lojban community, which can be found in Lojban Live Chat or on Google Groups. They will be happy to help.

In this tutorial, Lojban text is written in bold. Later, when Lojban loanwords are used in English sentences, they are not marked. Answers to exercises are displayed as a grey bar. Highlight the text in order to see it. English terms are written in italic.

Lastly, I have as far as possible attempted to use the Lojban words for grammatical constructs: sumka'i instead of pro-sumti, sumtcita instead of modal and jufra instead of utterance. This is because I feel the English words are often either arbitrary, in which case they are just more words to learn, or misleading, in which case they are worse than useless. In either case, as long as the words are specific to those who are learning Lojban anyway, there is no reason for them to exist as separate English words.

Lesson 0: Sounds

While you are (hopefully) eager to get started on the inner workings of Lojban grammar, a short lesson on the sounds and writing conventions of the language is beneficial. Learning a language only by reading is hard, and it's not easier if your internal voice is mispronouncing it.

For more details on vowels and consonants sounds used in Lojban, click on the letters described. They are pointing to Wikipedia articles which describe the sound and usually have an audio record of it.


There are five proper vowels in Lojban and one almost-vowel. First the proper ones:

a as in "father" or "large"
e as in "get" or "gem"
i as in "machine" or "scream" (not as in "hit")
o as in "bold" or "more" — not as in "so" (this should be a 'pure' sound.)
u as in "rude" or "due" (not as in "but")
y as "a" in "Tina" (not as in "but")

These are pretty much the same as vowels in Italian or Spanish. The sixth (almost-)vowel, y, is called a "schwa" in the language trade, and is pronounced as "comma", "taken" or "surprise!". It's the sound that comes out when the mouth is completely relaxed.

Two vowels together are pronounced as one sound (and called a "diphthong"). Some examples are:

ai as in "high"
au as in "how"
ei as in "hey"
oi as in "boy"
ia as in "yacht"
ie as in "yes"
iu as in "you"
ua as in "wander"
ue as in "wet"
uo as in "woke"
ui as in "we"

i and u act as semivowels when they precede another vowel. Double vowels are rare. The only examples are ii, which is pronounced like English "ye" (as in Oh come all ye faithful) or Chinese "yi", and uu, pronounced like "woo".

Note that because of variation between English dialects, approximations like these will necessarily be wrong for some speakers. The surest way to learn the phonology of the language is to imitate those who already speak it!


There are seventeen consonants in Lojban and one almost-consonant. The Lojban consonants are the same as the English, except that Lojban doesn't use the letters H, Q or W. Most of the consonants are pronounced like in English, but there are some exceptions:

g always "g" as in "gum", never "g" as in "gem"
c "sh", as in "ship"
j as in "measure" or French "bonjour"
x as in the exclamation "Ach!", or in German "Bach", Spanish "Jose" or Arabic "Khaled"

The almost-consonant is the apostrophe This letter is pronounced like the English letter H, but is only used between two vowels to prevent them from running into each other. Thus ui is normally pronounced "we", but u'i is "oohee". Groups of cmavo are called selma'o and are written using capital letters; but unexpectedly the capital version of this letter is h not H (ko'a is KOhA).

The combination dj is like the j in "joke". The combination tc is like the ch in "chat".

The following sound as they do in English, with the exception that r is often rolled (but does not have to be):

b, d, f, k, l, m, n, p, r, s, t, v, z.

Letter names

Speaking of the letters, what are the names for them? For example, when reciting the alphabet in English the letter C is pronounced "see". This is rather different than the sound the letter makes when used in a word. How about Lojban? Well, consonants are straightforward: The name of a consonant letter is the sound of that letter, plus y. So the consonant letters of Lojban, "b, c, d, f, g ...", are called by cy dy fy gy in Lojban. The almost-consonant ' is called .y'y (pronounced like an agreeing uh-huh but without the stress).

Vowels are handled by following the vowel sound with the word bu, which signifies we're speaking about a symbol. So the vowels of Lojban are: .abu .ebu .ibu .obu .ubu and .ybu.

Lastly you should know that stress is placed on the second-to-last syllable in words with more than one syllable, ignoring syllables containing y, and that one-syllable words are not stressed.

Correct pronunciation

You don't have to be very precise about Lojban pronunciation, because the phonemes are distributed so that it is hard to mistake one sound for another. This means that rather than one 'correct' pronunciation, there is a range of acceptable pronunciation—the general principle is that anything is OK so long as it doesn't sound too much like something else. For example, Lojban r can be pronounced like the "R" in English, Scottish or French.

Two things to be careful of, though, are pronouncing Lojban i and u like Standard British English "hit" and "but" (Northern English "but" is fine!). This is because non-Lojban vowels, particularly these two, are used to separate consonants by people who find them hard to say. For example, if you have problems spitting out the zd in zdani (house), you can say zɪdani — where the ɪ is very short, but the final i has to be long.

Writing Lojban

As you have already seen, Lojban uses the Latin alphabet, though various Lojbanists have suggested different, usually self-designed ones. Furthermore, Lojban almost always uses lower-case letters. Capital letters are only used to mark stress in proper names, but people tend to avoid them even in names.

Apart from the letters, some punctuation is used:

A full stop (period) is a glottal stop (the consonant in the middle of "uh-oh") or a short pause. The rules of Lojban make it easier for one word to run into another when the second word begins with a vowel; so any word starting with a vowel conventionally has a full stop placed in front of it. Full stops are not usually used to end sentences.

Commas are rare in Lojban. They are only used to emphasize boundaries between syllables, and adding or removing commas never changes a word's pronunciation or meaning.

The following are found writing styles of different Lojbanists, but they are not conventional:

Spaces are usually used between words. They are mandatory between some words (more on that in lesson thirteen). Double or triple space is sometimes used before the beginning of new sentences. This is to clearly mark sentence shift visually. This might compensate for lack of capital letters which are used for the same purpose in English.

In òrder to visuàlly reprèsent the stress on the penultìmate syllàble, and bècause they find it visuàlly plèasing, some pèople use grave or acute àccents òver the vòwel of those syllàbles.

Some people borrow other punctuation marks from English, even though they are not canon, and Lojban is equipped with actual words which should compensate for any punctuation one might want to use. Nonetheless, question marks, for example, clearly marks a sentence as a question and is much easier to catch with the eye than any word is, and so some Lojbanists use them. Quotation marks, parenthesis and exclamations marks can be used similarly. While this is not ungrammatical, since that doesn't interfere with the sentences, some people think exotic punctuation creates an unwanted difference between written and spoken Lojban, generally a big no-no.

Lojbanized foreign proper names (cmevla)

The following names are Lojbanized - their sounds are transcribed into Lojban and their ending sound have been changed to a consonant. The final consonant is necessary, because that's how foreign names are differentiated from Lojban words. Again, more on that in lesson thirteen.

Exercise 1

Where are these places?

  1. .nuIORK.
  2. .romas.
  3. .xavanas.
  4. .kardif.
  5. .beidjin.
  6. .ANkaras.
  7. .ALbekerkis.
  8. .vankuver.
  9. .keiptaun.
  10. .taibeis.
  11. .bon.
  12. .delis.
  13. .nis.
  14. .atinas.
  15. .lidz.
  16. .xelsinkis.


  1. New York: USA
  2. Rome: Italy
  3. Havana: Cuba
  4. Cardiff: Wales (The Welsh for "Cardiff" is "Caerdydd", which would Lojbanise to something like kairdyd..)
  5. Beijing: China
  6. Ankara: Turkey
  7. Albequerque: New Mexico, USA
  8. Vancouver: Canada
  9. Cape Town: South Africa
  10. Taipei: Taiwan (note b, not p. Although actually, the b in Pinyin is pronounced as a p... But this isn't meant to be a course on Mandarin!)
  11. Bonn: Germany
  12. Delhi: India (The Hindi for "Delhi" is "Dillî", which would give dilis. or dili'is..)
  13. Nice: France
  14. Athens: Greece ("Athina" in Greek)
  15. Leeds: England
  16. Helsinki: Finland

Exercise 2

Lojbanise the following names.

There are usually alternative spellings for names, either because people pronounce the originals differently, or because the exact sound doesn't exist in Lojban, so you need to choose between two Lojban letters. This doesn't matter, so long as everyone knows who or where you're talking about.

  1. John
  2. Melissa
  3. Amanda
  4. Matthew
  5. Michael
  6. David Bowie
  7. Jane Austen
  8. William Shakespeare
  9. Sigourney Weaver
  10. Richard Nixon
  11. Istanbul
  12. Madrid
  13. Tokyo
  14. San Salvador


  1. .djon. (or .djan. with some accents)
  2. .melisys.
  3. .amandys. (again, depending on your accent, the final y may be a, the initial a may be y, and the middle a may be e.)
  4. .matiius.
  5. .maikyl. or .maikl. , depending on how you say it.
  6. .deivyd.bauis. or .bouis.
  7. .djein.ostin.
  8. .uiliiam.cekspir.
  9. .sigornis.uivyr. or .sygornis.uivyr.
  10. .ritcyrd.niksyn.
  11. .istanBUL. with English stress, .IStanbul. with American, .istanbul. with Turkish. Lojbanists generally prefer to base cmevla on local pronunciation, but this is not an absolute rule.
  12. .maDRID.
  13. .tokiios.
  14. .san.salvaDOR. (with Spanish stress)


Lesson 1: Bridi, jufra, sumti and selbri

Bridi is the most central unit of Lojban utterances. The concept is very close to what we call a proposition in English. A bridi is a claim that some objects stand in a relation to each other, or that an object has some property. This stands in contrast to jufra, which are merely Lojban utterances, which can be bridi or anything else being said. The difference between a bridi and a jufra is that a jufra does not necessarily state anything, while a bridi does. Thus, a bridi might be true or false, while not all jufra can be said to be such.

To have some examples (in English, to begin with), Mozart was the greatest musician of all time is a bridi, because it makes a claim with a truth value, and it involves an object, Mozart, and a property, being the greatest musician of all time. On the contrary, Ow! My toe! is not a bridi, since it does not involve a relation, and thus does not state anything. Both, though, are jufra.

Try to identify the bridi among these English jufra:

  1. I hate it when you do that.
  2. Woah, that looks delicious!
  3. Geez, not again.
  4. No, I own three cars
  5. Nineteen minutes past eight.
  6. This Saturday, yes.

Answer: 1, 2 and 4 are bridi. The rest contain no relation or claim of a property.

Put in Lojban terms, a bridi consists of one selbri, and one or more sumti. The selbri is the relation or claim about the object, and the sumti are the objects which are in a relation. Note that object is not a perfect translation of sumti, since sumti can refer to not just physical objects, but can also purely abstract things like "The idea of warfare". A better translation would be something like "subject, direct or indirect object" for sumti, and main verb for selbri, though, as we will see, this is not optimal either.

We can now write the first important lesson down:

bridi = selbri + one or more sumti

Put another way, a bridi states that some sumti do/are something explained by a selbri.

Identify the sumti and selbri equivalents in these English jufra:

I will pick up my daughters with my car.

Answer: selbri: pick up (with). sumti: I, my daughters, my car

He bought 5 new shirts from Mark for just two hundred euro!

Answer: selbri: bought (from) (for) sumti: He, 5 new shirts, Mark and two hundred euros

Since these concepts are so fundamental to Lojban, let's have a third example:

So far, the EPA has done nothing about the amount of sulphur dioxide.

Answer: selbri: has done (about) sumti: The EPA, nothing and the amount of sulphur dioxide

Now try begin making Lojban bridi. For this you will need to use some words, which can act as selbri:

dunda = x1 gives x2 to x3 (without payment)
pelxu = x1 is yellow
zdani = x1 is a home of x2

Notice that these words meaning give, yellow and home would be considered a verb, an adjective and a noun in English. In Lojban, there are no such categories and no such distinction. dunda can be translated gives (verb), is a giver (noun), is giving (adjective) as well as to an adverb form. They all act as selbri, and are used in the same way.

As well as a few words, which can act as sumti:

mi = "I" or "we" – the one or those who are speaking
ti = "this" – a close thing or event nearby which can be pointed to by the speaker
do = "you" – the one or those who are being spoken to

See the strange translations of the selbri above - especially the x1, x2 and x3? Those are called sumti places. They are places where sumti can go to fill a bridi. Filling a sumti in a place states that the sumti fits in that place. The second place of dunda, for example, x2, is the thing being given. The third is the object which receives the thing. Notice also that the translation of dunda has the word to in it. This is because, while this word is needed in English to signify the receiver, the receiver is in the third sumti place of dunda. So when you fill the third sumti place of dunda, the sumti you fill in is always the receiver, and you don't need an equivalent to the word to!

To say a bridi, you simply say the x1 sumti first, then the selbri, then any other sumti.

Usual bridi: (x1 sumti) (selbri) (x2 sumti) (x3 sumti) (x4 sumti) (x5 sumti) (and so on)

The order can be played around with, but for now, we stick with the usual form. To say I give this to you you just say mi dunda ti do, with the three sumti at the right places.

So, how would you say This is a home of me?

Answer: ti zdani mi

Try a few more in order to get the idea of a place structure sink in.

You give this to me?

Answer: do dunda ti mi

And translate ti pelxu

Answer: This is yellow.

Quite easy once you get the hang of it, right?

Multiple bridi after each other are separated by .i This is the Lojban equivalent of full stop, but it usually goes before bridi instead of after them. It's often left out before the first bridi, though, as in all these examples:

.i = Sentence separator. Separates any two jufra (and therefore also bridi).

ti zdani mi .i ti pelxu This is a home to me. This is yellow.

Before you move on to the next lesson, I recommend that you take a break for at least seven minutes to let the information sink in.

Lesson 2: Skipping around with FA and zo'e

Most selbri have from one to five sumti places, but some have more. Here is a selbri with four sumti places:

vecnu = x1 sells x2 to x3 for price x4

If I want to say I sell this, it would be too much to have to fill the sumti places x3 and x4, which specify who I sell the thing to, and for what price. Luckily, I don't need to. sumti places can be filled with zo'e. zo'e indicates to us that the value of the sumti place is unspecified because it's unimportant or can be determined from context.

zo'e = something; fills a sumti place with something, but does not state what.

So to say I sell to you, I could say

mi vecnu zo'e do zo'e
I sell something to you for some price.

How would you say: That's a home (for somebody)?

Answer: ti zdani zo'e

How about (someone) gives this to (someone)?

Answer: zo'e dunda ti zo'e

Still, filling out three zo'e just to say that a thing is being sold takes time. Therefore you don't need to write all the zo'e in a bridi. The rule simply is that if you leave out any sumti, they will be considered as if they contained zo'e. If the bridi begins with a selbri, the x1 is presumed to be omitted and it becomes zo'e.

Try it out. What's Lojban for I sell?

Answer: mi vecnu

And what does zdani mi mean?

Answer: Something is a home of me or just I have a home.

As mentioned earlier, the form doesn't have to be {x1 sumti} {selbri} {x2 sumti} {x3 sumti} (ect.) In fact, you can place the selbri anywhere you want, just not at the beginning of the bridi. If you do that, the x1 is considered left out and filled with zo'e instead. So the following three jufra are all the exactly same bridi:

  • mi dunda ti do
  • mi ti dunda do
  • mi ti do dunda

Sometimes this is used for poetic effect. You sell yourself could be do do vecnu, which sounds better than do vecnu do. Or it can be used for clarity if the selbri is very long and therefore better be left at the end of the bridi.

There are also several ways to play around with the order of the sumti inside the bridi. The easiest one is by using the words fa, fe, fi, fo and fu.

fa = Tags the following sumti as filling x1
fe = Tags the following sumti as filling x2
fi = Tags the following sumti as filling x3
fo = Tags the following sumti as filling x4
fu = Tags the following sumti as filling x5

Notice that the vowels are the five vowels in the Lojban alphabet in order. Using one of these words marks that the next sumti will fill the x1, x2, x3, x4 and x5 respectively. The next sumti after that will be presumed to fill a slot one greater than the previous. To use an example:

dunda fa do fe ti doGiving by you of this thing to you. fa marks the x1, the giver, which is you. fe marks the thing being given, the x2. Sumti counting then continues from fe, meaning that the last sumti fills x3, the object receiving.

Attempt to translate the following three sentences:

mi vecnu fo ti fe do

Answer: I sell, for the price of this, you. or I sell you for the price of this (probably pointing to a bunch of money)

zdani fe ti

Answer: This has a home. Here, the fe is redundant.

vecnu zo'e mi ti fa do

Answer: You sell something to me for this price

Lesson 3: tanru and lo

In this lesson, you will become familiar with the concept of a tanru. A tanru is formed when a selbri is put in front of another selbri, modifying its meaning. A tanru is itself a selbri, and can combine with other selbri or tanru to form more complex tanru. Thus zdani vecnu is a tanru, as well as pelxu zdani vecnu, which is made from the tanru pelxu zdani and the single brivla word vecnu. To understand the concept of tanru, consider the English noun combination lemon tree. If you didn't know what a lemon tree was, but had heard about both lemons and trees, you would not be able to deduce what a lemon tree was. Perhaps a lemon-colored tree, or a tree shaped like a lemon, or a tree whose bark tastes like lemon. The only things you could know for sure would be that it would be a tree, and it would be lemon-like in some way.

A tanru is closely analogous to this. It cannot be said exactly what a zdani vecnu is, but it can be said that it is definitely a vecnu, and that it's zdani-like in some way. And it could be zdani-like in any way. In theory, no matter how silly or absurd the connection to zdani was, it could still truly be a zdani vecnu. However, it must actually be a vecnu in the ordinary sense in order for the tanru to apply. You could gloss zdani vecnu as home seller, or even better but worse sounding a home-type-of seller. The place structure of a tanru is always that of the rightmost selbri. It's also said that the left selbri modifies the right selbri.

"Really?", you'd ask, skeptically, "It doesn't matter how silly the connection to the left word in a tanru is, it's still true? So I could call all sellers for zdani vecnu and then make up some silly excuse why I think it's zdani-like?"

Well yes, but then you'd be a dick. Or at least you'd be intentionally misleading. In general, you should use a tanru when it's obvious how the left word relates to the right.

Attempt to translate the following: ti pelxu zdani do

Answer: That is a yellow home for you Again, we don't know in which way it's yellow. Probably it's painted yellow, but we don't know for sure.

mi vecnu dunda

Answer: I sell-like give. What can that mean? No idea. It certainly doesn't mean that you sold something, since, by definition of dunda, there can be no payment involved. It has to be a giveaway, but be sell-like in some aspect.

And now for something completely different. What if I wanted to say I sold to a German?

dotco = x1 is German/reflects German culture in aspect x2

I can't say mi vecnu zo'e dotco because that would leave two selbri in a bridi, which is not permitted. I could say mi dotco vecnu but that would be unnecessary vague - I could sell in a German way. Likewise, if I want to say I am friends with an American, what should I say?

pendo = x1 is a friend of x2
merko = x1 is American/reflect US culture in aspect x2

Again, the obvious would be to say mi pendo merko, but that would form a tanru, meaning I am friend-like American, which is wrong. What we really want to is to take the selbri merko and transform it into a sumti so it can be used in the selbri pendo. This is done by the two words lo and ku.

lo = generic begin convert selbri to sumti word. Extracts x1 of selbri to use as sumti.
ku = end convert selbri to sumti process.

You simply place a selbri between these two words, and it takes anything that can fill the x1 of that selbri and turns it into a sumti.

So for instance, the things that can fill zdani's x1 are only things which are homes of somebody. So lo zdani ku means a home or some homes for somebody. Similarly, if I say that something is pelxu, it means it's yellow. So lo pelxu ku refers to something yellow.

Now you have the necessary grammar to be able to say I am friends with an American. How?

Answer: mi pendo lo merko ku

There is a good reason why the ku is necessary. Try to translate A German sells this to me

Answer: lo dotco ku vecnu ti mi If you leave out the ku, you do not get a bridi, but simply three sumti. Since lo…ku cannot convert bridi, the ti is forced outside the sumti, the lo-construct is forced to close and it simply becomes the three sumti of lo dotco vecnu {ku}, ti and mi.

You always have to be careful with jufra like lo zdani ku pelxu. If the ku is left out the conversion process does not end, and it simply becomes one sumti, made from the tanru zdani pelxu and then converted with lo.

Lesson 4: Attitudinals

Another concept which can be unfamiliar to English speakers is that of attitudinals. Attitudinals are words that express emotions directly. They turned out to be incredibly awesome and useful. They all have a so-called free grammar, which means that they can appear almost anywhere within bridi without disrupting the bridi's grammar or any grammatical constructs.

In Lojban grammar, an attitudinal applies to the previous word. If that previous word is a word which begins a construct (like .i or lo), it applies to the entire construct. Likewise, if the attitudinal follows a word which ends a construct like ku, it applies to the ended construct.

Let's have two attitudinals to make some examples:

ui = attitudinal: simple pure emotion: happiness - unhappiness
za'a = attitudinal: evidential: I directly observe

Note that in the definition of ui, there are listed two emotions, happiness and unhappiness. This means that ui is defined as happiness, while its negation, means unhappiness. Negation might be the wrong word here. Technically, the other definition of ui is another construct, ui nai. Most of the time, the second definition of attitudinals - the ones suffixed with nai - really is the negation of the bare attitudinal. Other times, not so much.

nai = misc. negation - attached to attitudinals, it changes the meaning into the attitudinal's "negation"

And some more selbri, just for the heck of it:

citka = x1 eats x2
plise = x1 is an apple of strain/type x2

The sentence do citka lo plise ku ui, means You eat an apple, yay! (especially expressing that it is the apple that the speaker is happy about, not the eating, or the fact that it was you.) In the sentence do za'a citka lo plise ku, the speaker directly observes that it is indeed the you, who eats an apple as opposed to someone else.

If an attitudinal is placed at the beginning of the bridi, it is understood to apply to an explicit or implicit .i, thus applying to the entire bridi:

ui za'a do dunda lo plise ku miYay, I observe that you give an/some apple to me!

mi vecnu ui nai lo zdani ku I sell (which sucks!) a home.

Try it out with a few examples. First, though, here are some more attitudinals:

.u'u = attitudinal: simple pure emotion: guilt - remorselessness - innocence.
.oi = attitudinal: complex pure emotion: complaint - pleasure.
iu = attitudinal: miscellaneous pure emotion: love - hate.

Look at that, a word with three emotions in the definition! The middle one is accessed by suffixinng with cu'i. It's considered the midpoint of the emotion.

cu'i = attitudinal midpoint scalar: attach to attitudinal to change the meaning to the "midpoint" of the emotion.

Try saying I give something to a German, who I love

Answer: mi dunda fi lo dotco ku iu or zo'e instead of fi

Now Aah, I eat a yellow apple

Answer: .oi nai mi citka lo pelxu plise ku

Let's have another attitudinal of a different kind to illustrate something peculiar:

.ei = attitudinal: complex propositional emotion: obligation - freedom.

So, quite easy: I have to give the apple away is mi dunda .ei lo plise ku, right? It is, actually! When you think about it, that's weird. Why is it that all the other attitudinals we have seen so far expresses the speaker's feeling about the bridi, but this one actually changes what the bridi means? Surely, by saying I have to give the apple away, we say nothing about whether the apple actually is being given away. If I had used ui, however, I would actually have stated that I gave the apple away, and that I was happy about it. What's that all about?

This issue, exactly how attitudinals change the conditions on which a bridi is true, is a subject of a minor debate. The official, textbook rule, which probably won't be changed, is that there is a distinction between pure emotions and propositional emotions. Only propostional emotions can change the truth conditions, while pure emotions cannot. In order to express a propositional emotional attitudinal without changing the truth value of the bridi, you can just separate it from the bridi with .i. There is also a word for explicitly conserving or changing the truth conditions of a bridi:

da'i = attitudinal: discursive: supposing - in fact

Saying da'i in a bridi changes the truth conditions to hypothetical, which is the default using propositional attitudinals. Saying da'i nai changes the truth condition to the normal, which is default using pure attitudinals.

So, what's two ways of saying I give the apple away? (and feel obligation about it)

Answer: mi dunda lo plise ku .i .ei and mi dunda da'i nai .ei lo plise ku

The feeling of an attitudinal can be subscribed to someone else using dai. Usually in ordinary speech, the attitudinal is subscribed to the listener, but it doesn't have to be so. Also, because the word is glossed empathy (feeling others emotions), some Lojbanists mistakenly think that the speaker must share the emotion being subscribed to others.

dai = attitudinal modifier: empathy (subscribes attitudinal to someone else, unspecified)

Example: .u'i .oi dai citka ti - Ha ha, this was eaten! That must have hurt!

.u'i = attitudinal: simple pure emotion: amusement - weariness

What often used phrase could .oi .u'i dai mean?

Answer: Ouch, very funny.

And another one to test your knowledge: Try to translate He was sorry he sold a home (remembering, that tense is implied and need not be specified. Also, he could be obvious from context)

Answer: u'u dai vecnu lo zdani ku

Lastly, the intensity of an attitudinal can be specified using certain words. These can be used after an attitudinal, or an attitudinal with nai or cu'i suffixed. It's less clear what happens when you attach it to other words, like a selbri, but it's mostly understood as intensifying or weakening the selbri in some unspecified way:

Modifying word Intensity
cai Extreme
sai Strong
(none) Unspecified (medium)
ru'e Weak

What emotion is expressed using .u'i nai sai ?

Answer: Strong weariness

And how would you express that you are mildly remorseless?

Answer: .u'u cu'i ru'e

Lesson 5: Reordering places with SE

Before we venture into the territory of more complex constructs, you should learn another mechanism for reordering the sumti of a selbri. This, as we will show, is very useful for making description-like sumti (the kind of sumti with lo).

Consider the sentence I eat a gift, which might be appropriate if that gift is an apple. To translate this, it would seem natural to look up a selbri meaning gift before continuing. However, if one looks carefully at the definition of dunda, x1 gives x2 to x3, one realizes that the x2 of dunda is something given – a gift.

So, to express that sentence, we can't say mi citka lo dunda ku, because lo dunda ku would be the x1 of dunda, which is a donor of a gift. Cannibalism aside, we don't want to say that. What we want is a way to extract the x2 of a selbri.

This is one example where it is useful to use the word se. What se does is to modify a selbri such that the x1 and x2 of that selbri trade places. The construct of se + selbri is on its own considered one selbri. Let's try with an ordinary sentence:

ti se fanva mi = mi fanva ti
This is translated by me (= I translate this). [literally]
fanva = x1 translates x2 to language x3 from language x4 with result of translation x5

Often, but not always, bridi with se-constructs are translated to sentences with the passive voice, since the x1 is often the object taking action.

se has its own family of words. All of them swap a different place with the x1.

se swap x1 and x2
te swap x1 and x3
ve swap x1 and x4
xe swap x1 and x5

Note that s, t, v, and x are consecutive consonants in the Lojban alphabet.

So: Using this knowledge, what would ti xe fanva ti mean?

Answer: This is a translation of this (or fanva ti fu ti)

se and its family can of course be combined with fa and its family. The result can be very confusing indeed, if you wish to make it so:

klama = x1 travels/goes to x2 from x3 via x4 using x5 as transportation device

fo lo zdani ku te klama fe do ti fa mi = mi te klama do ti lo zdani ku and since te exchanges x1 and x3: = ti klama do mi lo zdani ku = This travels to you from me via a home.

Of course, no one would make such a sentence except to confuse people, or cruelly to test their understanding of Lojban grammar.

And thus, we have come to the point where we can say I eat a gift.. Simply exchange the sumti places of dunda to get the gift to be x1, then extract this new x1 with lo...ku. So, how would you say it?

One (possible) answer: mi citka lo se dunda ku

This shows one of the many uses for se and its family.

Lesson 6: Abstractions

So far we have only expressed single sentences one at a time. To express more complex things, however, you often need subordinate sentences. Luckily, these are much easier in Lojban than what one would expect.

We can begin with an example to demonstrate this:

I am happy that you are my friend.

Here, the main bridi is I am happy that X., and the sub-bridi is You are my friend. Looking at the definition for happy, which is gleki

gleki = x1 is happy about x2 (event/state)

we can see that the x2 needs to be an event or a state. This is natural, because one cannot be happy about an object in itself, only about some state the object is in. But alas! Only bridi can express a state or an event, and only sumti can fill the x2 of gleki!

As you might have guessed, there is a solution. The words su'u...kei is a generic convert bridi to selbri function, and works just like loku.

su'u = x1 is an abstraction of {bridi} of type x2
kei = end abstraction


melbi su'u dansu kei
Beautiful dancing/Beautiful dance
melbi = x1 is beautiful to x2.
dansu = x1 dances to accompaniment/music/rhythm x2.

It's usually hard to find good uses of a bridi as a selbri. However, since su'u BRIDI kei is a selbri, one can convert it to a sumti using lo...ku.

Now we have the equipment to express I am happy that you are my friend. Try it out!

pendo = x1 is a friend of x2

Answer: mi gleki lo su'u do pendo mi kei ku

However, su'ukei does not see much use. People prefer to use the more specific words nukei and du'ukei. They work the same way, but mean something different. nu…kei treats the bridi in between as an event or state, and du'u…kei treats it as an abstract bridi, for expressing things like ideas, thoughts or truths. All these words (except kei) are called abstractors. There are many of them, and only few are used much. su'u…kei is a general abstractor, and will work in all cases.

nu = x1 is an event of (bridi)
du'u = x1 is the predication of (bridi), as expressed in sentence x2

Use nu to say I'm happy about talking to you.

tavla = x1 talks to x2 about subject x3 in language x4.

Answer: mi gleki lo nu tavla do kei ku (notice both the English and the Lojban is vague as to who is doing the talking).

Other important abstractors include: ka...kei (property/aspect abstraction), si'o...kei (concept/idea abstraction), ni...kei (quantity abstraction) among others. The meanings of these is a complicated matter, and will be discussed much later, in lesson twenty-nine. For now, you'll have to do without them.

It is important to notice that some abstractors have several sumti places. As an example, du'u can be mentioned. du'u is defined:

du'u = abstractor. x1 is the predicate/bridi of (bridi) expressed in sentence x2.

The other sumti places besides x1 is rarely used, but lo se du'u (bridi) kei ku is sometimes used as a sumti for indirect quotation: I said that I was given a dog can be written mi cusku lo se du'u mi te dunda lo gerku ku kei ku, if you will pardon the weird example.

cusku = x1 expresses x2 to x3 through medium x4
gerku = x1 is a dog of race x2

Lesson 7: NOI

While we're at it, there's another type of subordinate bridi. These are called relative clauses. They are sentences which add some description to a sumti. Indeed, the "which" in the previous sentence marked the beginning of a relative clause in English describing relative clauses. In Lojban, they come in two flavors, and it might be worth distinguishing the two kinds before learning how to express them.

The two kinds are called restrictive and non-restrictive (or incidential) relative clauses. An example would be good here:

My brother, who is two meters tall, is a politician.

This can be understood in two ways. I could have several brothers, in which case saying he is two meters tall will let you know which brother I am talking about. Or I might have only one brother, in which case I am simply giving you additional information.

In English as well as Lojban we distinguish between these two kinds – the first interpretation is restrictive (since it helps restrict the possible brothers I might be talking about), the second non-restrictive. When speaking English, context and tone of voice (or in written English, punctuation) helps us distinguish between these two, but not so in Lojban. Lojban uses the constructs poi…ku'o and noi…ku'o for restrictive and non-restrictive relative clauses, respectively.

Let's have a Lojbanic example, which can also explain our strange gift-eating behavior in the example in lesson five:

noi = begin non-restrictive relative clause (can only attach to sumti)
poi = begin restrictive relative clause (can only attach to sumti)
ku'o = end relative clause
mi citka lo se dunda ku poi plise ku'o
I eat the gift that (something is) an apple.

Here the poi…ku'o is placed just after lo se dunda ku, so it applies to the gift. To be strict, the relative clause does not specify what it is, which is an apple, but given the context we can safely assume that it means that the gift is an apple. If we want to be absolutely sure that it indeed was the gift that was an apple, we use the word ke'a, which is a sumka'i (a Lojban pronoun, more on them later) representing the sumti which the relative clause is attached to. ke'a is often omitted for brevity when it would be in the x1 place of the relative clause.

ke'a = sumka'i; refers to the sumti, to which the relative clause it attached.
ui mi citka lo se dunda ku poi ke'a plise ku'o
Yay, I eat the gift that is an apple.

To underline the difference between restrictive and non-restrictive relative clauses, here's another example:

lojbo = x1 reflects Lojbanic culture/community is aspect x2; x1 is Lojbanic.
mi noi lojbo ku'o fanva fo lo lojbo ku
I, who am a Lojbanic, translate from some Lojbanic language.

Here, there is not multiple things which mi could refer to, and the fact that I am lojbanic is merely additional information not needed to identify me. Therefore noi…ku'o is appropriate.

See if you can translate this:

I flirt with the man who is beautiful/handsome.

nanmu = x1 is a man
melbi = x1 is beautiful to x2 in aspect (ka) x3 by standard x4
cinjikca = x1 flirts/courts x2, exhibiting sexuality x3 by standard x4

Answer: mi cinjikca lo nanmu ku poi (ke'a) melbi ku'o

On a more technical side note, it might be useful to know that lo (selbri) ku is often seen defined as zo'e noi ke'a (selbri) ku'o.

Besides, it is also possible to connect two or more relative clauses to the same sumti, by using the relative clause joiner zi'e. It's syntax is "sumti + relative clause + zi'e + relative clause (+ zi'e + relative clause (...))". Here is an example:

penmi = x1 meets/encounters x2 at/in location x3
dasni = x1 wears/is robed/garbed in x2 as a garment of type x3
mi tavla lo nanmu ku poi do penmi ke'a ku'o zi'e noi dasni lo xunre ku ku'o
I talked to the man that you met and which (incidentally) was dressed in red.
... and which wears something red... [literally]

Lesson 8: Terminator elision

je'u mi djica lo nu le merko poi tunba mi vau ku'o ku jimpe lo du'u mi na nelci lo nu ri darxi mi vau kei ku vau kei ku vau kei ku vau
I do wish the American, who is my sibling, would understand that I don't like that he hits me.

Regardless of whether the above sentence is being understood, (it shouldn't, as it contains words we have not covered in these lessons yet) one thing stands out: As more complex Lojban structures are learned, more and more of the sentences get filled with ku, kei, ku'o and other of those words which by themselves carry no meaning.

The function of all these words is to signal the end of a certain grammatical construct, like for instance convert selbri to sumti in the case of ku. The English word for this kind of word is terminator, the Lojban word is famyma'o. They are underlined in the example above.

Note: The vau in the above example are the famyma'o for end bridi. There is a good reason you have not yet seen it, stay tuned.

vau = famyma'o: terminates bridi.

In most spoken and written Lojban, most famyma'o are skipped (elided). This greatly saves syllables in speech and space in writing, however, one must always be careful when eliding famyma'o. In the simple example lo merko ku klama, removing the famyma'o ku would yield lo merko klama, which is a single sumti made from the tanru merko klama. Thus, it means an American traveler instead of an American travels. famyma'o elision can lead to very wrong results if done incorrectly, which is why you haven't learned about it until now.

The rule for when famyma'o can be elided is very simple, at least in theory: You can elide a famyma'o, if and only if doing so does not change the grammatical constructs in the sentence. In other words, a construct extends as far right as possible, until either its famyma'o or another word not allowed in the construct appears.

Most famyma'o can be safely elided at the end of the bridi. Exceptions are the obvious ones like end quote-famyma'o and end bridi grouping-famyma'o. This is why vau is almost never used – simply beginning a new bridi with .i will almost always terminate the preceding bridi anyway. It has one frequent use, however. Since attitudinals always apply to the preceding word, applying it to a famyma'o applies it to the entire construct which is terminated. Using vau, one can then use attitudinals afterthought and apply them to the entire bridi:

za'a do dunda lo zdani {ku} lo prenu {ku}... vau .i'e
I see that you give a home to a person... I approve!
prenu = x1 is a person; x1 has a personality.

Knowing the basic rules for famyma'o elision, we can thus return to the original sentence and begin removing famyma'o:

je'u mi djica lo nu le merko poi tunba mi vau ku'o ku jimpe lo du'u mi na nelci lo nu ri darxi mi vau kei ku vau kei ku vau kei ku vau

We can see that the first vau is grammatically unnecessary, because the next non-famyma'o-word is jimpe, which is a selbri. Since there can only be one selbri per bridi, vau is not needed. Since jimpe as a selbri cannot be in the relative clause either (only one bridi in a clause, only one selbri in each bridi), we can elide ku'o. Likewise, jimpe cannot be a second selbri inside the construct le merko poi{...}, so the ku is not needed either. Furthermore, all the famyma'o at the very end of the sentence can be elided too, since beginning a new bridi will terminate all of these constructs anyway.

We then end up with:

je'u mi djica lo nu le merko poi tunba mi jimpe lo du'u mi na nelci lo nu ri darxi mi

with no famyma'o at all!

When eliding famyma'o, it is a good idea to be acquainted with cu. cu is one of those words which can make your (Lojbanic) life a lot easier. What it does is to separate any previous sumti from the selbri. One could say that it defines the next word to be a selbri, and terminates exactly as much as it needs to in order to do that.

cu = elidable marker: separates selbri from preceding sumti, allows preceding famyma'o elision.
prami = x1 loves x2
lo su'u do cusku lo se du'u do prami mi vau kei ku vau kei ku se djica mi
= lo su'u do cusku lo se du'u do prami mi cu se djica mi

That you say that you love me is desired by be = I wish you said you loved me.

Note: cu is not a famyma'o, because it is not tied to one specific construct. But it can be used to elide other famyma'o.

One of the greatest strengths of cu is that it quickly becomes easy to intuitively understand. By itself it means nothing, but it reveals the structure of Lojban expressions by identifying the core selbri. In the original example with the violent American brother, using cu before jimpe does not change the meaning of the sentence in any way, but might make it easier to read.

In the following couple of lessons, cu will be used when necessary, and all famyma'o elided if possible. The elided famyma'o will be encased in curly brackets, as shown below. Try to translate it!

.a'o do noi ke'a lojbo .o'a dai {ku'o} cu jimpe lo du'u lo famyma'o {ku} cu vajni {vau} {kei} {ku} {vau}

vajni = x1 is important to x2 for reason x3
jimpe = x1 understands that x2 (du'u-abstraction) is true about x3
a'o = attitudinal: simple propositional emotion: Hope - despair
o'a = attitudinal: simple propositional emotion: pride - modesty/humility - shame
dai = attitudinal modifier: Empathy (subscribes attitudinal to someone else, unspecified)

What do I state?

Answer: I hope that you, a proud Lojbanist, understands that famyma'o are important

Fun side note: Most people well-versed in famyma'o-elision do it so instinctively that they often must be reminded how important understanding famyma'o are to the understanding of Lojban. Therefore, each Tuesday have been designated Terminator Day or famyma'o djedi on the Lojban IRC chatroom. During Terminator Day, many people try (and often fail) to remember writing out all famyma'o with some very verbose conversations as a result.

Lesson 9: sumtcita

So far we have been doing pretty well with the selbri we have had at hand. However, there is a finite amount of defined selbri out there, and in many cases the sumti places are not useful for what we had in mind. What if, say, i want to say that I am translating using a computer? There is no place in the structure of fanva to specify what tool I translate with, since, most of the time, that is not necessary. Not to worry, this lesson is on how to add additional sumti places to the selbri.

The most basic way to add sumti places are with fi'o SELBRI fe'u (yes, another example of a famyma'o, fe'u. It's almost never necessary, so this might be the last time you ever see it.)

In between these two words goes a selbri, and like lo SELBRI ku, fi'o SELBRI fe'u extracts the x1 of the selbri put into it. However, with fi'o SELBRI fe'u, the selbri place is converted, not to a sumti, but to a sumtcita, meaning sumti-label, with the place structure of the x1 of the selbri it converted. This sumtcita then absorbs the next sumti. One could say that using a sumtcita, you import a sumti place from another selbri, and add it to the bridi being said.

Note: Sometimes, especially in older texts, the term tag or modal is used for sumtcita. Ignore those puny English expressions. We teach proper Lojban here.

While it is hard to grasp the process from reading about it, an example can perhaps show its actual simplicity:

skami = x1 is a computer for purpose x2
pilno = x1 uses x2 as a tool for doing x3

mi fanva ti fi'o se pilno {fe'u} lo skami {ku}{vau} - I translate this with a computer The x2 of pilno, which is the x1 of se pilno is a place structure for a tool being used by someone. This place structure is captured by fi'o SELBRI fe'u, added to the main selbri, and then filled by lo skami. The idea of sumtcita is sometimes expressed in English using the following translation:

I translate this with-tool: A computer

A sumtcita can only absorb one sumti, which is always the following one. Alternatively, one can use the sumtcita construct by itself without sumti. In this case you need to put it either before the selbri or terminate it with ku. In such case one can think as if the sumtcita has the word zo'e as the sumti.

zukte = x1 is a volitional entity carrying out action x2 for purpose x3
zarci = x1 is a market/store/exchange/shop(s) selling/trading (for) x2, operated by/with participants x3

fi'o zukte {fe'u} ku lo prenu {ku} cu klama lo zarci {ku}{vau} - By their own volition, a person is going to the store

Note that there is ku in fi'o zukte {fe'u} ku. Without it the sumtcita would have absorbed lo prenu {ku} and we don't want that.

We can say the same in other words:

fi'o zukte {fe'u} zo'e lo prenu {ku} cu klama lo zarci {ku}{vau}

lo prenu {ku} cu fi'o zukte fe'u klama lo zarci {ku}{vau}

retaining the meaning.

What does mi jimpe fi lo skami fi'o se tavla {fe'u} mi state?

Answer: I understand something about computers, spoken to me

Putting the sumtcita right in front of the selbri also makes it self-terminate, since sumtcita only can absorb sumti, and not selbri. This fact will be of importance in next lesson, as you will see.

Actually, fi'o is not used very often despite its flexibility. What IS used very often, though, are BAI. BAI is a class of Lojban words, which in themselves act as sumtcita. An example of this is zu'e, the BAI for zukte. Grammatically, zu'e is the same as fi'o zukte fe'u. Thus, the above example could be reduced to:

zu'e ku lo prenu {ku} cu klama lo zarci {ku}{vau}. There exist something like 60 BAI, and a lot of these are very useful indeed. Furtermore, BAI can also be converted with se and friends, meaning that se zu'e is equal to fi'o se zukte fe'u, which results in a great deal more BAI.

Lesson 10: PU, FAhA, ZI, VA, ZEhA, VEhA

How unfamiliar a language like Lojban must seem to an English-speaker, when one can read through nine lessons of Lojban grammar without meeting a tense once! This is because, unlike many natural languages (most Indo-European ones, for instance), all tenses in Lojban are optional. Saying mi citka lo cirla {ku} can mean I eat cheese or I ate the cheese or I always eat cheese or In a moment, i will have just finished eating cheese. Context resolves what is correct, and in most conversation, tenses are not needed at all. However, when it's needed it's needed, and it must be taught. Furthermore, Lojban tenses are unusual because they treat time and space fundamentally the same - saying that I worked a long time ago is not grammatically different than saying I work far away to the north.

Like many other languages, the Lojban tense system is perhaps the most difficult part of the language. Unlike many other languages though, it's perfectly regular and makes sense. So fear not, for it will not involve sweating to learn how to modify the selbri or anything silly like that.

No, in the Lojban tense system, all tenses are sumtcita, which we have conveniently just made ourselves familiar with. Okay okay, technically, tenses are slightly different from other sumtcita, but this difference is almost insignificant, and won't be explained until later. In most aspects they are like all other sumtcita; they are terminated by ku, making it explicit that PU is terminated by ku.

There are many different kinds of tense-sumtcita, so let's start at the ones most familiar to English-speakers.

pu = sumtcita: before {sumti}
ca = sumtcita: at the same time as {sumti}
ba = sumtcita: after {sumti}

These are like the English concepts before, now and after. In actuality though, one could argue that two point-like events can never occur exactly simultaneously, rendering ca useless. But ca extends slightly into the past and the future, meaning just about now. This is because human beings don't perceive time in a perfectly logical way, and the Lojban tense system reflects that.

Side note: It was actually suggested making the Lojban tense system relativistic. That idea, however, was dropped, because it is counter-intuitive, and would mean that to learn Lojban, one would have to learn the theory of relativity first.

So, how would you say I express this (pointing to a paper) after I came to this place?

Answer: mi cusku ti ba lo nu mi klama ti {vau} {kei} {ku} {vau}

Usually when speaking, we do not need to specify which event in the past this action is relative to. In: I gave a computer away, we can assume that the action happened relative to now, and thus we can elide the sumti of the sumtcita, because it's obvious:

pu ku mi dunda lo skami {ku} {vau} or

mi dunda lo skami {ku} pu {ku} {vau} or, more commonly

mi pu {ku} dunda lo skami {ku} {vau}. The sumti which fills the sumtcita is an implied zo'e, which is almost always understood as relative to the speaker's time and place (this is especially important when speaking about left and right). If speaking about some events that happened some other time than the present, it is sometimes assumed that all tenses are relative to that event which is being spoken about. In order to clarify that all tenses are relative to the speaker's current position, the word nau can be used at any time. Another word, ki marks a tense which is then considered the new standard. That will be taught way later.

nau = updates temporal and spacial frame of reference to the speaker's current here and now.
gugde = x1 is the country of people x2 with land/territory x3

Also note that mi pu {ku} klama lo merko gugde {ku} {vau}, I went to America, does not imply that I'm not still traveling to USA, only that it was also true some time in the past, for instance five minutes ago.

As mentioned, spacial and temporal time tenses are very much alike. Contrast the previous three time tenses with these four spacial tenses:

zu'a = sumtcita: left of {sumti}
ca'u = sumtcita: in front of {sumti}
ri'u = sumtcita: right of {sumti}
bu'u = sumtcita: at the same place as {sumti} (spacial equivalent of ca)
.o'o = attitudinal: complex pure emotion: patience - tolerance - anger

What would .o'o nai ri'u ku lo prenu {ku} cu darxi lo gerku {ku} pu {ku} {vau} mean?

darxi = x1 beats/hits x2 with instrument x3 at locus x4

Answer: {anger!} To the right (of something, probably me) and in the past (of some event), something is an event of a person beating a dog. or A man hit a dog to my right!

If there are several tense sumtcita in one bridi, the rule is that you read them from left to right, thinking it as a so called imaginary journey, Where you begin at an implied point in time and space (default: the speaker's now and here), and then follow the sumtcita one at a time from left to right.


mi pu {ku} ba {ku} jimpe fi lo lojbo famyma'o {ku} {vau} = At some time in the past, I will be about to know about famyma'os.

mi ba {ku} pu {ku} jimpe fi lo lojbo famyma'o {ku} {vau} At some point in the future, I will have understood about famyma'os.

Since we do not specify the amount of time we move back or forth, the understanding could in both cases happen in the future or the past of the point of reference.

Also, if spacial and temporal tenses are mixed, the rule is to always put temporal before spacial.

Suppose we want to specify that the a man hit a dog just a minute ago. The words zi, za and zu specifies a short, unspecified (presumably medium) and long distance in time. Notice the vowel order i, a and u. This order appears again and again in Lojban, and might be worth to memorize. Short and long in are always context dependent, relative and subjective. Two hundred years is a short time for a species to evolve, but a long time to wait for the bus.

zi = sumtcita: Ocurring the small distance of {sumti} in time from point of reference
za = sumtcita: Ocurring the unspecified(medium) distance of {sumti} in time from point of reference
zu = sumtcita: Ocurring the far distance of {sumti} in time from the point of reference

Similarly, spacial distance is marked by vi, va and vu for short, unspecified (medium) and long distance in space.

vi = sumtcita: Ocurring the small distance of {sumti} in space from point of reference
va = sumtcita: Ocurring the unspecified(medium) distance of {sumti} in space from point of reference
vu = sumtcita: Ocurring the far distance of {sumti} in space from the point of reference
gunka = x1 works at x2 with objective x3

Translate: ba {ku} za ku mi vu {ku} gunka {vau}

Answer: Some time in the future, I will work a place far away

Note: People rarely use zi, za or zu without a pu or ba in front of it. This is because most people always need to specify past or future in their native language. When you think about it Lojbanically, most of the time the time-direction is obvious, and the pu or ba superfluous!

The order in which direction-sumtcita and distance-sumtcita are said makes a difference. Remember that the meanings of several tense words placed together are pictured by an imaginary journey reading from left to right. Thus pu zu is a long time ago while zu pu is in the past of some point in time which is a long time toward the future or the past of now. In the first example, pu shows that we begin in the past, zu then that it is a long time backwards. In the second example, zu shows that we begin at some point far away in time from now, pu then, that we move backwards from that point. Thus pu zu is always in the past. zu pu could be in the future. The fact that these time tenses combine in this way is one of the differences between tense sumtcita and other sumtcita. The meanings of other sumtcita are not altered by the presence of additional sumtcita in a bridi.

As briefly implied earlier, all these constructs basically treat bridi as if they were point-like in time and space. In actuality, most events play out over a span of time and space. In the following few paragraphs, we will learn how to specify intervals of time and space.

ze'i = sumtcita: spanning over the short time of {sumti}
ze'a = sumtcita: spanning over the unspecified (medium) time of {sumti}
ze'u = sumtcita: spanning over the long time of {sumti}
ve'i = sumtcita: spanning over the short space of {sumti}
ve'a = sumtcita: spanning over the unspecified (medium) space of {sumti}
ve'u = sumtcita: spanning over the long space of {sumti}

Six words at a time, I know, but remembering the vowel sequence and the similarity of the initial letter z for temporal tenses and v for spacial tenses might help the memorizing.

.oi = attitudinal: pain - pleasure

Translate: .oi dai do ve'u {ku} klama lo dotco gugde {ku} ze'u {ku} {vau}

Answer: Ouch, you spend a long time traveling a long space to Germany

ze'u and its brothers also combine with other tenses to form compound tenses. The rule for ze'u and the others are that any tenses preceding it marks an endpoint of the process (relative to the point of reference) and any tenses coming after it marks the other endpoint relative to the first. This should be demonstrated with a couple of examples:

.o'ocu'i do citka pu {ku} ze'u {ku} ba {ku} zu {ku} {vau} - {tolerance} you eat beginning in the past and for a long time ending at some point far into the future of when you started or Hmpf, you ate for a long time. One can also contrast do ca {ku} ze'i {ku} pu {ku} klama {vau} with do pu {ku} ze'i {ku} ca {ku} klama {vau}. The first event of traveling has one endpoint in the present and extends a little towards the past, while the second event has one endpoint in the past and extends only to the present (that is, slighty into the past or future) of that endpoint.

jmive = x1 is alive by standard x2

What does ui mi pu {ku} zi {ku} ze'u {ku} jmive {vau} express?

Answer: {happiness!} I live from a little into the past and a long way towards the future or past (obviously the future, in this case) of that event or I am young, and have most of my life ahead of me :)

Just to underline the similarity with spacial tenses, let's have another example, this time with spacial tenses:

.u'e = attitudinal: wonder - commonplace

.u'e za'a bu'u {ku} ve'u {ku} ca'u {ku} zdani {vau} - What does it mean?

Answer: {wonder} {I observe!} Extending a long space from here to my front is a home. or Wow, this home extending ahead is huge!

Before we continue with this syntax-heavy tense system, i recommend spending at least ten minutes doing something which doesn't occupy your brain in order to let the information sink in. Sing a song or eat a cookie very slowly - whatever, as long as you let your mind rest.

Lesson 11: ZAhO

Though we won't go through all Lojban tense constructs for now, there is one other kind of tense that I think should be taught now. These are called event contours, and represent a very different way of viewing tenses that we have seen so far. So let's get to it:

Using the tenses we have learned so far, we can imagine an indefinite time line, and we then place events on that line relative to the now. With event contours, however, we view each event as a process, which has certain stages: A time before it unfolds, a time when it begins, a time when it is in process, a time when it ends, and a time after it has ended. Event contours then tells us which part of the event's process was happening during the time specified by the other tenses. We need a couple of tenses first:

pu'o = sumtcita: event contour: Bridi has not yet happened during {sumti}
ca'o = sumtcita: event contour: Bridi is in process during {sumti}
ba'o = sumtcita: event contour: The process of bridi has ended during {sumti}

This needs to be demonstrated by some examples. What's ui mi pu'o {ku} se zdani {vau} mean?

Answer: Yay, I'm about to have a home.

But hey, you ask, why not just say ui mi ba {ku} se zdani {vau} and even save a syllable? Because, remember, saying that you will have a home in the future says nothing about whether you have a home now. Using pu'o, though, you say that you are now in the past of the process of you having a home, which means that you don't have one now.

Note, by the way, that mi ba {ku} se zdani {vau} is similar to mi pu'o {ku} se zdani {vau}, and likewise with ba'o and pu. Why do they seem reversed? Because event contours view the present as seen from the viewpoint of the process, whereas the other tenses view events seen from the present.

Often, event contours are more precise that other kind of tenses. Even more clarity is achieved by combining several tenses: .a'o mi ba {ku} zi {ku} ba'o {ku} gunka {vau} - I hope I've soon finished working.

In Lojban, we also operate with an event's natural beginning and its natural end. The term natural is highly subjective in this sense, and the natural end refers to the point in the process where it should end. You can say about a late train, for instance, that its process of reaching you is now extending beyond its natural end. An undercooked, but served meal, similarly, is being eaten before that process' natural beginning. The event contours used in these examples are as follows:

za'o = sumtcita: event contour: Bridi is in process beyond its natural end during {sumti}
xa'o = sumtcita: event contour: Bridi is immaturely in process during {sumti}
cidja = x1 is food, which is edible for x2

Translate: .oi do citka za'o lo nu do ba'o {ku} u'e citka zo'e noi cidja do {vau} {ku'o} {vau} {kei} {ku}

Answer: Oy, you keep eating when you have finished, incredibly, eating something edible!


Image above: ZAhO tenses (event contours). All tenses above the line of the event signify stages covering an amount of time. All tenses below the event line signify stages which are point-like.

All of these tenses have been describing stages of a process which takes some time (as shown on the graph above; those tenses above the event like). But many of the event contours describes point like stages in the process, like its beginning. As is true of ca and bu'u, they actually extend slightly into the past and future of that point, and need not to be precise.

The two most important point-like event contours are:

co'a = sumtcita: event contour: Bridi is at its beginning during {sumti}
co'u = sumtcita: event contour: Bridi is at its ending during {sumti}

Furthermore, there is a point where the process is naturally complete, but not necessarily has ended yet:

mo'u = sumtcita: event contour: Bridi is at its natural ending during {sumti}

Most of the time, though, processes actually end at their natural ending; this is what makes it natural. Trains are not usually late, and people usually retrain themselves to eat only edible food.

Since a process can be interrupted and resumed, these points have earned their own event contour also:

de'a = sumtcita: event contour: Bridi is pausing during {sumti}
di'a = sumtcita: event contour: Bridi is resuming during {sumti}

In fact, since jundi means x1 pays attention to x2, de'a jundi and di'a jundi are common Lojban ways of saying BRB and back. One could of course also say the event contours by themselves and hope the point gets across.

Finally, one can treat an entire event, from the beginning to the end as one single point using co'i:

penmi = x1 meets x2 at location x3

mi pu {ku} zi {ku} co'i {ku} penmi lo dotco prenu {ku} {vau} - A little while ago, I was at the point in time where i met a German person

Lesson 12: Orders and questions

Phew, those two long lessons with syntax heavy Lojban gives the brain something to ponder about. Especially because it's so different from English. So let's turn to something a little lighter: Orders and questions.

What the... sit up and focus!

Since the way to express orders in English is to leave out the subject of the clause, why did you assume that it was you I was speaking to, and not ordering myself, or expressing the obligation someone else has? Because the English language understands that orders, by their very nature, are always directed towards the listener - the you, and so the subject is not necessary.

In Lojban, eliding the subject yields zo'e, so that possibility is sadly not open to us. Instead, we use the word ko, which is the imperative form of do. Grammatically and bridi-wise, it's equivalent to do, but it adds a layer of semantics, since it turns every statement with ko in it into an order. Do such that this sentence is true for you=ko! For the same reason we don't need the subject in English sentences, we don't need order-words derived from any other sumti than do.

How could you order one to go far away for a long time (using klama as the only selbri?)

Answer: ko ve'u ze'u klama

(.i za'a dai a'o mi ca co'u ciska lo famyma'o .i ko jimpe vau .ui) - work it out. Note that

ciska = x1 writes text x2 on x3

Questions in Lojban are very easy to learn, and they come in two kinds: Fill in the blank, and true/false questions. Let's begin with the true-false question kind - that's pretty overcomeable, since it only involves one word, xu.

xu works like an attitudinal in the sense that it can go anywhere, and it applies to the preceding word (or construct). It then transforms the sentence into a question, asking whether it is true or not. In order to affirm, you simply repeat the bridi:

xu ze'u zdani do .i ze'u zdani mi, or you just repeat the the selbri, which is the bridi with all the sumti and tenses elided: zdani.

There is an even easier way to affirm using brika'i, but those are a tale for another time. To answer no or false, you simply answer with the bridi negated. That too, will be left for later, but we will return to question answering by then.

The other kind of question is fill in the blank. Here, you ask for the question word to be replaced for a construct, which makes the bridi correct. There are several of these words, depending on what you are asking about:

ma = sumti question
mo = selbri question
xo = number question
cu'e = tense question

As well as many others. To ask about a sumti, you then just place the question word where you want your answer: do dunda ma mi - asks for the x2 to be filled with a correct sumti. You give what to me?. The combination of sumtcita + ma is very useful indeed:

mu'i = sumtcita: motivated by the abstraction of {sumti}

.oi do darxi mi mu'i ma - Oy, why do you hit me?!

Let's try another one. This time, you translate:

ui dai do ca ze'u pu mo

Answer: You're happy, what have you been doing all this long time until now? Technically, it could also mean what have you been?, but answering with ua nai li'a remna (Uh, human, obviously) is just being incredibly annoying on purpose.

Since tone of voice or sentence structure does not reveal whether a sentence is a question or not, one better not miss the question word. Therefore, since people tend to focus more on words in the beginning or at the end of sentences, it's usually worth the while to re-order the sentence so that the question words are at those places. If that is not feasable, pau is an attitudinal marking that the sentence is a question. Contrary, pau nai explicitly marks any question as being rhetorical.

While we are on the topic of questions, it's also appropriate to mention the word kau, which is a marker for indirect question. What's an indirect question, then? Well, take a look at the sentence: mi djuno lo du'u ma kau zdani do - I know what is your home.

djuno = x1 knows fact(s) x2 are true about x3 by epistemology x4

One can think it as the answer to the question ma zdani do. More rarely, one can mark a non-question word with kau, in which case one still can imagine it as the answer to a question: mi jimpe lo du'u dunda ti kau do - I know what you have been given, it is this.

Lesson 13: Morphology and word classes

Back to more heavy (and interesting) stuff.

If you haven't already, I strongly suggest you find the Lojbanic recording called "Story Time with Uncle Robin", or listen to someone speak Lojban on Mumble, and then practice your pronunciation. Having an internal conversation in your head in Lojban is only good if it isn't with all the wrong sounds, and learning pronunciation from written text is hard. Therefore, this lesson will not be on the Lojban sounds, however important they might be, but a short introduction to the Lojban morphology.

What is morphology? The word is derived from Greek meaning the study of shapes, and in this context, we talk about how we make words from letters and sounds, as contrasted with syntax - how we make sentences with words. Lojban operates with different morphological word classes, which are all defined by their morphology. To make it all nice and systematic though, words with certain functions tend to be grouped by morphological classes, but exceptions may occur.

Class Meaning Defined By Typical Function
brivla bridi-word Among first 5 letters (excluding ) is a consonant cluster. Ends in vowel. Acts as a selbri by default. Always has a place structure.
gismu Root-word 5 letters of the form CVCCV or CCVCV One to five sumti places. Covers basic concepts.
Lujvo Compound word. Derived from from lujvla, meaning complex word Min. 6 letters. Made by stringing rafsi together with binding letters if necessary. Covers more complex concepts than gismu.
zi'evla Free-word As brivla, but do not meet defining criteria of gismu or lujvo, ex: angeli Covers unique concepts like names of places or organisms.
cmevla Name-word Beginning and ending with pause (full stop). Last sound/letter is a consonant. Always acts as a name or as the content of a quote.
cmavo Grammar-word. From cmavla, meaning small word One consonant or zero, always at the beginning. Ends in a vowel. Grammatical functions. Varies
rafsi Affix CCV, CVC, CV'V, -CVCCV, -CCVCV, CVCCy- or CCVCy- Not actual words, but can be stringed together to form lujvo
  • cmevla are very easy to identify because they begin and end with a pause, signaled by a full stop in writing, and the last letter is a consonant. Cmevla have two functions: They can either act as a proper name, if prefixed by the article la (explained in next lesson), or they can act as the content of a quote. As previously stated, one can mark stress in the names by capitalizing the letters which are stressed. Examples of cmevla are: .io'AN. (Johan), .mat. (Matt) and .cumindzyn. (Xuming Zeng). Names which do not end in consonants have to have one added: .anas. (Anna), or removed: .an.
  • brivla are called bridi-words because they by default are selbri, and therefore almost all Lojban words with a place structure are brivla. This has also given them the English nickname content-words. It's nearly impossible to say anything useful without brivla, and almost all words for concepts outside lojban grammar (and even most of the words for things in the language) are captured by brivla. As shown in the table, brivla has three subcategories:
  • gismu are the root words of the language. Only about 1450 exist, and very few new ones are added. They cover the most basic concepts like circle, friend, tree and dream. Examples include zdani, pelxu and dunda
  • lujvo are made by combining rafsi (see under rafsi), respresenting gismu. By combining rafsi, one narrows down the meaning of the word. lujvo are made by an elaborate algorithm, so making valid lujvo on the fly is near impossible, with few exceptions like selpa'i, from se prami, which can only have one definition. Instead, lujvo are made once, its place structure defined, and then that definition is made official by the dictionary. Examples include brivla (bridi-word), cinjikca (sexual-socializing = flirting) and cakcinki (shell-insect = beetle).
  • zi'evla are made by making up words which fit the definition for brivla, but not for lujvo or gismu. They tend to cover concepts which it's hard to cover by lujvo, for instance names of species, nations or very cultural specific concepts. Examples include xanguke (South Korea) cidjrpitsa (pizza) or .angeli (angel).
  • cmavo are small words with one or zero consonants. They tend to not signify anything in the exterior world, but to have only grammatical function. Exceptions occur, and it's debatable how much attitudinals exists for their grammatical function. Another weird example are the words of the class GOhA, which act as brivla. It is valid to type several cmavo in a row as one word, but in these lessons, that won't be done. By grouping certain cmavo in functional units, though, it is sometimes easier to read. Thus, uipuzuvukumi citka is valid, and is parsed and understood as ui pu zu vu ku mi citka. Like other Lojban words, one should (but need not always) place a full stop before any words beginning with a vowel.
    • cmavo of the form xVV, CV'VV or V'VV are experimental, and are words which are not in the official language definition, but which have been added by Lojban users to respond to a certain need.
  • rafsi are not Lojban words, and can never appear alone. However, several (more than one) rafsi combine to form lujvo. These must still live up to the brivla-definition, for instance lojban is invalid because it ends in a consonant (which makes it a cmevla), and ci'ekei is invalid because it does not contain a consonant cluster, and is thus read as two cmavo written as one word. Often, a 3-4 letter string is both a cmavo and a rafsi, like zu'e, which is both the BAI and the rafsi for zukte. Note that there is nowhere that both a cmavo and a rafsi would be grammatical, so these are not considered homophones. All gismu can double as (word-final) rafsi, if they are prefixed with another rafsi. The first four letter of a gismu suffixed with an "y" can also act as a rafsi, if they are suffixed with another rafsi. The vowel "y" can only appear in lujvo or cmevla. Valid rafsi letter combinations are: CVV, CV'V, CCV, CVCCy- CCVCy-, -CVCCV and -CCVCV.

Using what you know now, you should be able to answer the test I thus present:

Categorize each of the following words as cmevla (C), gismu (g), lujvo (l), zi'evla (z) or cmavo (c):

A ) jai G ) mumbl
B ) .irci H ) .i'i
C ) bostu I ) cu
D ) xelman J ) plajva
E ) po'e K ) danseke
F ) djisku L ) .ertsa

Answer: a-c, b-z, c-g, d-C, e-c, f-l, g-C, h-c, i-c, j-l, k-z, l-z. I left out the full stops before and after names in order not to make the task too easy. Note: some of these words, like bostu do not exist in the dictionary, but this is irrelevant. The morphology still makes it a gismu, so it's just an undefined gismu. Similarly with .ertsa

Lesson 14: Lojban sumti 1ː LE and LA

If you have read and understood the content of all the lessons until now, you have amassed a large enough knowledge of Lojban so that it doesn't matter in which order you learn the rest. As a result, the order of the next lessons will be a mixture of sorted by increasing difficulty and sorted by importance in ordinary Lojban conversation.

One of the biggest constrains on your speak now is your limited knowledge on how to make sumti. So far, you only know ti and lo SELBRI, which doesn't take you far considering how important sumti are in Lojban. This lesson as well as the following two will be about the Lojban sumti. For now, we focus on the descriptive-like sumti, the ones made with articles like lo

Articles are in lojban called gadri, and all the ones discussed in this lesson are terminated by ku, except the combination LA CMEVLA. We will begin by describing three simple kinds of descriptive sumti, and then immediately find that they are not so simple after all:

lo = gadri: generic, converts selbri to sumti.
le = gadri: specific and descriptive, converts selbri to sumti.
la = gadri: naming article, convert selbri or cmevla to sumti.

You are already familiar with lo and what it does. lo creates a sumti referring to what fits in the first place of the following selbri.

This may be contrasted with le, which is specific and descriptive. Saying le gerku says that you have one or more specific objects in mind, and you use the selbri gerku to describe it, so that the listener may identify those specific objects. This means that le has two important differences from lo: Firstly, it cannot refer to objects in general, but always refers to specific objects. Secondly, le gerku explicitly hints that the selbri is only meant to help the speaker identify what the description refers to, whether or not it actually satisfies the selbri. Perhaps the speaker is referring to a hyena, but is not familiar with them and thinks dog is a good enough approximation to be understood; however, this non-veridicality is perhaps over-emphasized in many texts. The best way to describe a dog is usually to describe it as being a dog, and unless there is a good reason not to, le gerku is usually presumed to refer to something which is also lo gerku.

In translation, lo gerku can be any of the dog, the dogs, a dog, some dogs, or dogs in general, while le gerku is the dog or the dogs. Even better for le gerku would be the dog(s)

Last of the three basic gadri, there is la, the naming gadri, which strips the following selbri of its usual meaning and refers to someone or something whose name is that selbri. If I in English refer to a person called Innocent by her name, I neither describe her as being innocent, nor do I state that she is. I only state that by convention, that object is referred to by that selbri or cmevla. Note that la and the gadri derived from it can convert cmevla to sumti unlike any other gadri. Also: Be cautious: Other texts do not mention that names can be formed from ordinary selbri using the gadri la. But those heretics must burn; selbri names are as good as they get, and many a proud Lojbanist have them.

la is a bit eccentric, since it always marks the beginning of a name. Unlike the other gadri, anything that can be grammatically placed after la and its sisters are considered part of the name. For example, le mi gerku is "my dog", but la mi gerku is someone or something called "My Dog".

These three basic gadri can be expanded with three more, which correspond to the previous:

loi = gadri: generic, mass of individuals
lei = gadri: specific and descriptive, mass of individuals
lai = gadri: mass of named individuals

These are the same as the first three articles in all aspects except for one: they wrap the sumti into masses. Masses are used to abstract multiple individuals into single entities for ease of expression. For example, a football team can be described as a mass of its members, or an animal as a mass of cells.

mivysle = x1 is a biological cell of organism x2
remna = x1 is a human

loi mivysle cu remna - "Masses of cells are humans". Again, none of the cells are humans. Indeed, the cells have very few human traits, but the cells considered as a whole makes up a human. This example also shows that the selbri following loi must be satisfied by the members of the mass, but not by the mass itself: a human isn't a cell either.

A mass made with lei, such as lei gerku, refers to a mass formed by a group of specific individuals, which the speaker refers to as le gerku.

It needs to be noted that regular sumti built using lo are usually sufficient even when a selbri is meant to apply collectively. Constructing masses is mainly necessary when talking about multiple groups of individuals.

sruri = x1 flanks/encircles/encloses x2 in line/plane/directions x3

lo prenu cu sruri lo zdaniPeople surround the house. The Lojban sentence shares the obvious meaning of the English one, namely that people are arranged around the house, not necessarily that individual people are stretched around it.

But what if we want to explicitly say that people surround the house from head to toe? In order to be explicit about a selbri distributing across individuals, one needs lo, le or la with an outer quantifier. The subject of quantifiers will be considered later, in lesson twenty-two.

Lastly, there are the (only two) generalizing gadri:

lo'e = gadri: veridical convert selbri to sumti. Sumti refers to the archetype of lo {selbri}.
le'e = gadri: Descriptive convert selbri to sumti. Sumti refers to the described/perceived archetype of le {selbri}.

Of which there is no la-equivalent.

So, what is actually meant by the archetype? For lo'e tirxu, it is an ideal, imagined big cat, which has all the properties which best exemplifies big cats. It would be wrong to say that this includes having a striped fur, since a big systematic subgroup of the members of the set of big cats do not have striped fur, such as the leopards and the jaguars. Likewise, the typical human does not live in Asia even though a lot of humans do. However, if sufficiently many humans have a trait, for instance being able to speak, we can say:

kakne = x1 is capable of doing/being x2 under circumstance x3

lo'e remna cu kakne lo nu tavla - The typical human being can speak.

le'e then, is the ideal object as perceived or described by the speaker. This need not be factually correct, and is often translated as the stereotype, even though the English phrase have some unpleasant negative connotations, which the Lojban does not. In fact, everyone has a stereotypical archetypichal image of any category. In other words, lo'e remna is the archetype which best exemplifies all lo remna, while the archetype le'e remna best exemplifies all le remna.

The eleven gadri can be seen in the diagram below.

Generic Masses Generalizing
Veridical lo loi lo'e
Descriptive le lei le'e
Name la lai does not exist

Note: Earlier, there was a word xo'e for the generic gadri. However, the rules and definitions for gadri were changed in late 2004, and the current set of rules on this topic, nicked xorlo has replaced the old way. Now, lo is generic, and xo'e is used as an elliptical digit (lesson nineteen). There are also gadri for building sets (lo'i, le'i, la'i), but they are exceedingly rare in post-xorlo usage.

Lesson 15: Lojban sumti 2ː KOhA3, KOhA5 and KOhA6

See what happens if I try to translate the sentence: Stereotypical people who can speak Lojban speak to each other about the languages they can speak:

bangu = x1 is a language used by x2 to express x3 (abstraction)

le'e prenu poi ke'a kakne lo nu tavla fo la .lojban. cu tavla le'e prenu poi ke'a kakne lo nu tavla fo la .lojban. lo bangu poi lo prenu poi ke'a tavla fo la .lojban. cu se bangu ke'a

What we see is that the Lojban version is much longer than the English. This is primarily because the first, ridiculously long sumti is being repeated two more times in the Lojban text, while the English can refer to it by each other and they - much more efficiently. Wouldn't it be clever if Lojban somehow had mechanisms for doing the same?

It turns out it does, what a surprise! Lojban has a range of words called sumka'i meaning sumti-representatives. In English, we refer to them as pro-sumti, because they are essentially the same as the English pronouns, but with sumti instead of nouns. In fact, you already know ti, do and mi, but there are many more, so let's get learning. First, we want to put it into system. We can begin with the ones most familiar to English, and what you've already learned:

ti = sumka'i: immediate ‘it': represents a sumti physically near the speaker'
ta = sumka'i: nearby ‘it': represents a sumti some physical distance from the speaker OR close to the listener'
tu = sumka'i: distant ‘it': represents a sumti physically far from the speaker and the listener.'

You can again recognize the i, a, u-sequence which pops up over and over. Some things might take some clearing up, though. Firstly, these sumti can represent anything which can be said to occupy a physical space. Objects, certainly. Ideas, certainly not. Events are accepted, but only to the extent they are restricted to a specific place - the Jasmin Revolution cannot be pointed at, but some bar-fight or a kiss might. Secondly, note that the distance is relative to different things for the different words: tu only applies if it's distant from both the speaker and the listener. In cases where the speaker and listener is far apart and the listener cannot see the speaker talking, ta refers to something close to the listener. Thirdly, it's all relative and context dependent. These three words are all problematic in written text, for instance, because the position of the speaker and listener is unknown to each other, and changes as time goes by. Furthermore, the author of a book cannot point to an object and express the pointing in the book.

Then there is a series called KOhA3, to which mi and do (and ko, but I won't write that here) belongs:

mi = sumka'i: The speaker(s).
mi'o = sumka'i: The mass of the speaker(s) and the listener(s) .
mi'a = sumka'i: The mass of the speaker(s) and others.
ma'a = sumka'i: The mass of the speaker(s), the listener(s) and others.
do = sumka'i: The listener(s).
do'o = sumka'i: The mass of the listener(s) and others.

These six sumka'i are more easily grasped in the below Venn diagram:


Venn diagram of KOhA3 (ko excluded). le drata is not a KOhA3, but means the other(s)

It is possible for several people to be the speakers, if one statement is made on the behalf of all of them. Therefore, while we can be translated as either mi, mi'o, mi'a or ma'a, what one quite often means is really just mi. All of these six, if they refer to more than one individual, represent masses. Within bridi-logic, the bridi mi gleki said by speaker A is exactly equivalent to do gleki said by speaker B to speaker A, and are considered the same bridi. We will come back to this later, in the brika'i (pro-bridi) lesson.

All of these sumka'i are very content-specific, and cannot be used, for instance, to help us with the sentence which this lesson began with. The following series can in principle be used to refer to any sumti:

ri = sumka'i: Last sumti mentioned'
ra = sumka'i: A recent, but not the last sumti mentioned'
ru = sumka'i: A sumti mentioned long ago'

These sumti will refer to any terminated sumti except most other sumka'i. The reason that most other sumka'i cannot be referred to by these sumti, is that they are so easy to just repeat by themselves. The exception to the rule are ti, ta and tu, because you could have changed what you point at, and thus cannot just repeat the word. (There are some other exceptions, to be handled later.) They will only refer to terminated sumti, and thus cannot, for instance, be used to refer to an abstraction if the word in is that abstraction: le pendo noi ke'a pendo mi cu djica lo nu ri se zdani - here ri cannot refer to the abstration, since it is not terminated, nor to mi or ke'a, since they are sumka'i, so it refers to le pendo.

ra and ru are context-dependent in what they refer to, but they follow the rules mentioned above, and ru always refer to a more distant sumti than ra, which is always more distant than ri.

ri and it's brothers are pretty well suited for dealing with the original sentence. Try saying it using two instances of sumka'i!

Answer: le'e prenu poi ke'a kakne lo nu tavla fo la .lojban. cu tavla ru lo bangu poi ru cu se bangu ke'a. ri is not correct, because it refers to la .lojban.. ra could be used, but could be mistakenly be thought to refer to lo nu tavla fo la .lojban., but ru is assumed to refer to the most distant sumti - the most outer one.

Lastly, there a sumtcita which represent utterances: So called utterance variables. They need not be restricted to one sentence (jufra), but can be several sentences, if the context allows it:

da'u = Utterance variable: Remote past sentence
de'u = Utterance variable: Recent sentence
di'u = Utterance variable: Previous sentence
dei = Utterance variable: This sentence
di'e = Utterance variable: Next sentence
de'e = Utterance variable: Near future sentence
da'e = Utterance variable: Remote future sentence
do'i = Utterance variable: Elliptical utterance variable: Some sentence

These represents sentences as sumti, and refer only to the spoken words or the letters, not to the meaning behind them.

There are more Lojban sumka'i, but for now you probably need a break from them. The next lesson will be on derived sumti, sumti made from other sumti.

Lesson 16: Lojban sumti 3ː derived sumti

You can probably see that the sumti le bangu poi mi se bangu ke'a is a less than elegant expression for my language. This is because it's really a work around. A language which I speak can be said to fill into the x1 of the bridi bangu mi. We can't convert that to a sumti using a gadri: le bangu {ku} mi is two sumti, because bangu mi is a bridi, not a selbri. Neither can we convert it using le su'u, because the su'u gives the bridi a new x1, the abstraction, and the le then extracts that. That makes an abstraction sumti meaning something like that something is my language.

Enter be. be is a word which binds constructs (sumti, sumtcita and others) to a selbri. Using it in ordinary selbri has no effect: in mi nelci be do, the be does nothing. However, when a sumti is bound to a selbri this way, you can use a gadri on the selbri without the sumti splitting off: le bangu be mi is a correct solution to the problem above. Likewise, you can attach a sumtcita: le jinga be gau do: The one who wins because of you.

What if I want to attach several sumti to a selbri inside a gadri? The giver of the apple to you is le dunda be lo plise be do, right? Nope. The second be attaches to the apple, meaning le plise be do - The apple of the strain of you, which makes no sense. In order to string several sumti to a selbri, the all the ones following the first must be bound with bei. The binding can be terminated with be'o - one instance of be'o for each selbri which has sumti bound by be.

To list them:

be = binds sumti or sumtcita to selbri
bei = binds a second, third, fourth (ect) sumti or sumtcita to a selbri
be'o = ends binding to selbri

There is also ways to loosely associate a sumti with another. pe and ne for restrictive and non-restrictive association. Actually, le bangu pe mi is a better translation of my language, since this phrase, like the English, is vague as to how the two are associated with each other.

pe and ne are used as loose association only, like saying my chair about a chair which you sit on. It's not really yours, but has something do to with you. A more intimate connection can be established with po, which makes the association unique and binding to a person, as in my car for a car that you actually own. The last kind of associator is po'e, which makes a so-called "inalienable" bond between sumti, meaning that the bond is innate between the two sumti. Some examples could be "my mother", "my arm" or "my home country"; none of these "possesions" can be lost (even if you saw off your arm, it's still your arm), and are therefore inalienable. Almost all of the times a po'e is appropriate, though, the x2 of the selbri contains the one to which the x1 is connected, so be is better.

ne = non-restrictive relative phrase. "which is associated with..."
pe = restrictive relative phrase. "which is associated with..."
po = possesive relative phrase. "which is specific to..."
po'e = inalienable relative phrase. "which belongs to..."

A very useful construct to know is {gadri} {sumti} {selbri}. this is equivalent to {gadri} {selbri} pe {sumti}. For instance le mi gerku is equivalent to le gerku pe mi. One could have description sumti inside description sumti, saying le le se cinjikca be mi ku gerku, = le gerku pe le se cinjikca be mi =the dog of the man I'm flirting with, but that's not very easy to read (or to understand when spoken), and is often being avoided.

One need also to learn tu'a, since it will make a lot of sentences much easier. It takes a sumti and converts it to another sumti - an elliptical abstraction which has something to do with the first sumti. For example, I could say mi djica lo nu mi citka lo plise, or I could let it be up to context what abstraction about the apple I desire and just say mi djica tu'a lo plise. One always has to guess what abstraction the speaker means by tu'a SUMTI, so it should only be used when context makes it easy to guess. Another example:

gasnu = x1 does/brings about x2 (volition not implied)

za'a do gasnu tu'a lo skami - I see that you make the computer do something. Officially, tu'a SUMTI is equivalent to le su'u SUMTI co'e. Vague, but useful. There are situations where you cannot use tu'a, even though it would seem suitable. These situations are when I don't want the resulting sumti to be an abstraction, but a concrete sumti. In this case, one can use zo'e pe.

tu'a = convert sumti to vague abstraction involving the sumti. Equivalent to le su'u SUMTI co'e kei ku

Finally, one kind of sumti can be turned into another by the words of the class LAhE.

lu'a = Convert individual(s)/mass/sequence/set to individuals.
lu'i = Convert individual(s)/mass/sequence/set to a set.
lu'o = Convert individual(s)/mass/sequence/set to mass.
vu'i = Convert individual(s)/mass/sequence/set to sequence; the order is not stated.

The use of these words is straight-forwardly: Placing them before a sumti of a certain type makes a new sumti of a new type. Notice, though, that as a fourth kind of sumti, a sequence has been introduced. This is not used very often (it doesn't have its own gadri, for instance), but just included here for completion.

The last two members of LAhE do not convert between types of sumti, but allows you to speak of a a sumti by only mentioning something which references to it:

If one sumti A refers to a sumti B, for instance because sumti A is a title of a book, or a name, or a sentence (which always refer to something, at least a bridi), la'e SUMTI A refers to sumti B. For instance, mi nelci la'e di'u for I like what you just said (not mi nelci di'u which just means I like your previous sentence) or la'e le cmalu noltru for the book The Little Prince, and not some little prince himself. The cmavo lu'e does the exact reverse – lu'e SUMTI refers to an object which refers to the sumti.

la'e = "the thing referred to by" - extracts a sumti A from a sumti B which refers to A.
lu'e = "the thing referring to" - extracts a sumti B from a sumti A, when B refers to A.

Lesson 17: Cute assorted words

And with that, third chapter, you know a lot about Lojban sumti. After such a long time of rigorous systematic learning, what could be more fitting that this lesson where I speak about some words which I could not, or wanted not to fit into any other lessons? So here are a few small and really useful words:

The following cmavo are all elliptical words. You should already be familiar with the first.

zo'e = elliptical sumti
co'e = elliptical selbri
do'e = elliptical sumtcita
ju'a = elliptical evidential
do'i = elliptical utterance variable
ge'e = elliptical attitudinal

All of these act grammatically as a cmavo of the kind they represent, but they contain no information, and can be quite handy when you're lazy and don't need to be specific anyway. There are, however, a few things which need to be cleared up:

  • zo'e have to refer to something which is claimed to have a value. zero cars or nothing, for instance, has no value, and therefore cannot be referred to by zo'e. This is because, if it could mean nothing by zo'e, then any selbri could be identical to its negation, if one of the elided sumti were filled with a zo'e with no value.
  • ge'e does not mean that you feel no emotion, just that you feel nothing special or worth to mention at the moment. It's similar to I'm fine.. ge'e pei ask about an elliptical emotion and is a good translation for: How are you feeling?.
  • co'e is handy when needing a selbri in a construct for grammatical reasons, like in the definition of tu'a in the previous lesson.
  • ju'a does not change the truth value or subjective understanding of the bridi or anything like that. In fact, it's mostly does nothing. However, ju'a pei, What is your basis for saying that? is handy.
  • do'i is really useful. A lot of times when you refer to utterances or conversations by words like this or that, you want do'i.
  • If you fill in more sumti than a selbri has places for, the last sumti have implied do'e sumtcita in front of them.

Furthermore, there is a word, zi'o, that you can fill a sumti place with to delete it from any selbri. lo melbi be zi'o, for instance, is just Something beautiful, and does not include the usual x2 of melbi, which is the observer who judges something to be beautiful. Thus, it can mean something like Objectively beautiful. It does not state that nothing fills the sumti place which is being deleted, just that the sumti place is not being considered in the selbri. Using zi'o with a sumtcita gives weird results. Formally, they should cancel each other out. Practically, it would probably be understood as an explicit way of saying that the sumtcita does not apply, as in: mi darxi do mu'i zi'o - I hit you, with or without motivation.

Then there is the word jai. It's one of those cool, small words which are hard to grasp, but easy to work with once you know it. It has two distinct, but similar functions. Both have something to do with converting the selbri, like se does.

jai = Selbri conversion: Converts sumtcita or unspecified abstraction to x1. Use with fai
fai = Marks sumti place. Works like fa. To be used with jai.

The first grammatical construction it can make is "jai {sumtcita} {selbri}". It changes the sumti places such that the sumti place of the sumtcita becomes the selbri's x1, and the selbri's old x1 is removed, and only accessible by using fai, which works like fa. You can see it with this example:

gau = sumtcita (from gasnu) bridi has been brought about by/with active agent {sumti}'

do jai gau jundi ti fai mi. - You bring about attention to this by me. The new selbri, jai gau jundi, has the place structure of x1 brings about attention paid to x2. These are then filled by do and ti. The fai then marks the place for the old x1, the one who was paying attention, and it is filled with mi. This word can be very convenient and has tons of uses. A good example is descriptive-like sumti. One can, for instance, refer to the method of volitional action by lo jai ta'i zukte.

ta'i = sumtcita (from tadji): Bridi is done with the method of {sumti}

Can you deduce what the ordinary Lojban phrase do jai gau mo means?

Answer: What are you doing?

The other function of jai is easier to explain. It simply converts the selbri such that the sumti in the x1 gets a tu'a in front of it (ko'a jai broda = tu'a ko'a broda). In other words, it converts the selbri in a way such that it builds an elliptical abstraction from the sumti in the x1, and then fills x1 with the abstraction instead of the actual sumti. Again, the original sumti place is accessible by fai.

A very active Lojban IRC-user often says le gerku pe do jai se stidi mi, to use a random example of a sumti in x1. What's he saying?

stidi = x1 inspires/suggests x2 in/to x3

Answer: I suggest (something about) your dog.

So far you've learned how to convert bridi to selbri, selbri to sumti, and selbri into bridi, since all selbri by themselves are also bridi. You only need one last function: convert sumti to selbri. This is done with the word me. It accepts a sumti and converts it into a selbri.

me = Generic convert sumti to selbri. x1 is/are among the referents of SUMTI

When screwing a sentence up, knowing how to correct yourself is a good idea. There are three words in Lojban which you can use to delete your previous word(s)

si = deletion: Deletes last word only.
sa = deletion: Deletes back until next cmavo spoken.
su = deletion: Deletes entire discourse.

The function of these words are obvious: They delete words as if they have never been spoken. They do not work inside certain quotes (all quotes except lu...li'u), though, as that would leave it impossible to quote these words. Several si in a row deletes several words

Lesson 18: Quotes

One of the key design features of Lojban is that it's supposed to be audio-visual isomorphic, meaning that everything expressed in text should also be expressed in speech and vice versa. Therefore, there cannot be any punctuation which is not pronounced. This means that Lojban has a wide range of words to quote other words. All Lojban quotes take some input of text and converts it to a sumti. Let's begin with the most simple:

lu = Quote word: Begin quote of grammatical Lojban content
li'u = Quote word: End quote of grammatical Lojban content

The text inside this construct must by itself be grammatical. It can quote all Lojban words with some few exceptions, most notably, obviously, li'u.

Try to translate the following sentence. Take your time.

mi stidi lo drata be tu'a lu ko jai gau mo li'u

drata = x1 is different from x2 by standard

Answer: I suggest something different than something about ko jai gau mo.

These quote words cannot quote ungrammatical text. This is sometimes useful, when you want to only pick out part of a sentence, as in: is gi'e a Lojban sumtcita?

For this, you need these two cmavo

lo'u = Quote word: Begin quote of ungrammatical but Lojban content
le'u = Quote word: End quote of ungrammatical but Lojban content

The text inside must be Lojban words, but need not be grammatical. Try to translate the above example (the one with gi'e) into Lojban

Answer: xu lo'u gi'e le'u lojbo sumtcita

This quote can be used to quote all Lojban words except le'u. However, this is not enough. If we want to translate is do mo a correct translation of "What's up?", we might be slightly wrong about what we here state, since do mo also can mean What are you?, but let's roll with it for a second. What we need here is the word zoi.

zoi = Next cmavo starts all-purpose quote and closes all-purpose quote.

When using zoi, you pick any morphologically correct lojban word at will (called the delimiter), which then opens a quote. To close it, use that word again. This way, you can quote anything except the delimiter, which shouldn't be a problem because you can pick it yourself. Usually, the word picked is either zoi itself, or a letter which stands for the language which the quote is written in. Example: I liked The Phantom of the Opera is mi pu nelci la'e zoi zoi. The Phantom of the Opera .zoi Notice two things: Firstly, I need a la'e, since I didn't like the quote, but rather what it referred to. Secondly, between the chosen delimiter and the quote, there are pauses, optionally represented by a full stop in writing. This pause is necessary to correctly identify the delimiter.

Try to translate the above sentence concerning What's up?

drani = x1 is correct/proper in aspect x2 in situation x3 by standard x4

Answer: xu lu do mo li'u drani xe fanva zoi gy. What's up? .gy. Here the delimiter gy is chosen because it's short for glico, meaning "English"

Closely analogously, there is la'o. It works exactly like zoi, but turns the resulting quote into a name. It is needed because normally, only selbri and cmevla can be names, not quotes.

la'o = Next cmavo is begin all-purpose quote and close all-purpose quote – use as name.

Last of the official quote words, there is zo. zo always quotes the next Lojban word, no matter what it is. It's pretty handy.

zo = quotes next Lojban word, no matter what.


zo zo zo'o plixau
"zo" is useful, hehe.
zo'o = attitudinal: discursive: Humorously, "kidding you"
plixau = x1 is useful for x2 to do purpose x3

Some Lojban users have found it useful to supplement with four additional quote words. The most used is:

u'i ri pu cusku zo'oi Doh
Ha ha, he said "Doh!"
zo'oi = Quote next word only. Next word is identified by pauses in speech or whitespace/dot in writing:

It is apparently very easy to use, but as a matter of fact, general use of them is very problematic. Users should be aware that the word following zo'oi should not include a period, a glottal stop or a pause. For example, * zo'oi http://www.lojban.org/ is not grammatical since the string "http://www.lojban.org/" contains periods.

Another erratic text: * lo salpo (ku) fa'u lo finti cu smuni zo'oi saka fa'u zo'oi sa.ka lo ponjo. Here "sa.ka" has a period inside.

Analogous to zo'oi and la'o, there is also the word la'oi, which works just like zo'oi, but forms a sumti that refers to something called (whatever next words is put):

la'oi = Scope over the next word only; "something called by the name...". Next word is identified by pauses in speech or whitespace/dot in writing.

How would you say: "Safi" is an English guy. It's his name?

glico = x1 is English/pertains to English culture in aspect x2
cmene = x1 is the name of x2 as used by x3

Answer: la'oi Safi glico .i lu'e ri cmene ri

la'oi has the same problem as zo'oi: the word following la'oi should not include a period, a glottal stop or a pause. For example, the following sentences are not grammatical:

  • .u'a mi te vecnu lo zgike datni pe la'oi t.A.T.u. Here "t.A.T.u" has periods inside ("t.A.T.u" was a musical group).

Example of spoken text: la'oi .uli.uli zgike tutci. "`uli`uli" is a Hawaiian musical instrument. This word has periods inside.

Example of spoken text: ju'i la'oi jugemujugemugokounosurikirekaijarisuigiono- suigioumatsu,unraimatsufuuraimatsuku,unerutokoronisumutokoro,iaburakoujinoburakouji- paipopaipopaiponosiu,uringansiu,uringan,nogu,urindaigu,urindainoponpokopi,inoponpokona,anotcoukiu,umeinotcousuke mi'o ko'oi klama lo ckule. Don't take a breathing in the name, or it will result in an error! This word ("じゅげむじゅげむごこうのすりきれかいじゃりすいぎょのすいぎょうまつうんらいまつふうらいまつくうねるところにすむところやぶらこうじのぶらこうじぱいぽぱいぽぱいぽのしゅーりんがんしゅーりんがんのぐーりんだいぐーりんだいのぽんぽこぴーのぽんぽこなーのちょうきゅうめいのちょうすけ") is a famous Japanese name of a boy.)

Thirdly, ra'oi quotes the next rafsi. Since rafsi are not words, they would usually have to be quoted by zoi. Furthermore, several rafsi are also cmavo. To avoid confusion of which is meant, ra'oi always refer to a rafsi, and is wrong in front of any text string which are not rafsi.

What does ra'oi zu'e rafsi zo zukte .i ku'i zo'oi zu'e sumtcita mean?

ku'i = attitudinal: discursive: However / though (contrasts to something previously said)
rafsi = x1 an affix for word/concept x2 with properties/of form x3 in language x4

Answer: The rafsi zu'e is a rafsi for zukte. But zu'e is a sumtcita.

And finally the useful word ma'oi. ma'oi quotes any cmavo, but treats the quote as a name for the word class (selma'o) to which that word belongs. So, for instance, ba'o belongs to the wordclass called ZAhO, so ma'oi ba'o is unofficial Lojban for the selmaho ZahO.

Try it out. Say that pu and ba are in the same selma'o!

cmavo = x1 is a grammatical word of class x2 in language x3

One possible answer: zo pu cmavo ma'oi ba

Lesson 19: Numbers

When learning a language, one of the things which are usually taught very early on is how to count. This really makes little sense, because it's not necessary to know numbers if you don't know how to speak about those things to which they apply. This is partly the reason why I have left it for lesson number nineteen. The other reason is that while the numbers themselves are easy to learn, how they apply to sumti can get very confusing indeed. That, however, we will save for a later lesson.

Before learning the words themselves, you should know that numbers do not have any internal grammar. This means that any row of number words (henceforth referred to as a "number string") are treated identically to any other number string to the Lojban grammar, even if the string makes no sense. Therefore, one can never answer unambiguously whether a number construct makes sense or not. There are, however, intended ways of using the number words, and confusion will probably result if you deviate from the standard.

Learning all the number words of Lojban are way beyond the scope of this lesson, so you will only be introduced to what is normally used in text. The wide range of Lojban mathematical cmavo are called mekso (Lojban for "mathematical expression"), and is widely disregarded because of its complexity and questionable advantage over so-called bridi math.

Let's begin with the ordinary Lojban numbers, from zero to nine:

Notice how the vowels are alternating (with the exception of no), and how no consonant is used for two digits. In order to express numbers higher than nine, the numbers are just strung together:
  • vo mu ci – four hundred and fifty three (453)
  • pa no no no no ten thousand (10 000)
There is also a question-digit, which is used like other fill-in-the-blank question words. It's xo. The answer to such a question may be just the relevant digit(s) by itself, or they can be numerical constructs, as shown later.
  • ci xo xo xo – "Three thousand and how many?" (3???)
xo = question digit – use like any other digit to ask for the correct digit.
The experimental word xo'e is sometimes used to mean an unspecified, elliptical digit. Its definition is not official, though.
  • ci xo'e xo'e xo'e – Three thousand and something
xo'e = elliptical digit.
Since all number strings are treated grammatically the same, one might also answer several digits to one xo'e Furthermore, there is also a set of hexadecimal digits A through F. By default, Lojban operates in base 10, but when using hexadecimal digits, it can be safely assumed that you use base sixteen:
dau fei gai jau rei xei vai
10(A) 11(B) 12(C) 13(D) 14(E) 14(E) 15(F)

Yes, I know there are two words for E. The official one is rei (all three-letter cmavo beginning with x is experimental). xei was invented to avoid confusion with re.

The base can be explicitly stated using ju'u: Any number before ju'u the number being spoken of, any number after is the base of the number:

  • dau so fei no ju'u pa re – A9B0 in base 12 (notice here that base 12 is always in decimal. It is possible to permanently change the base you speak in, but since it has never been used in practice, it has not been standardized how one should do it)

Fractions are also useful to learn how to express. They are usually expressed via a decimal point, pi.

pi = Decimal point (or point in whichever base you are talking in)

pa re pi re mu – twelve point two five (12.25).

Like in mathematics, when no number string is placed before or after pi, zero is assumed.

Related to this, the number separator pi'e is used to separate numbers, either to separate digits when speaking in a base larger than sixteen, or when a decimal point is not applicable, for instance, when talking about time in hours, minutes, seconds:

pa so pi'e re mu pi'e no ju'u re ze – Nineteen, twenty-five, zero in base 27 (JP0 base 27)

re re pi'e vo bi – twenty-two, fourty eight (22:48)

There is also a range of number words which are not mathematically exact but rather subjective or relative. The behaviors of these words are almost exactly like the behavior of digits, except they cannot be combined to make bigger numbers the way digits can:

ro so'a so'e so'i so'o so'u
all almost all most many some few

When combined with any of the digits, these words are assumed to give a second verdict about the size of the number:

mu bi so'i sai – Fifty eight, which is really many.

They should therefore not be placed in the middle of a number string. When placed after pi, they are assumed to convey the size of a fraction:

  • pi so'u – a small part of it
  • pi so'o – some of it
  • pi so'i – a large part of it
  • pi so'e – most of it
  • pi so'a – almost all of it

These are some hightly subjective numbers - they work just like the previous ones.

du'e mo'a rau
too many too few enough

The following five are context-based numbers – these work like the previous ones, with the exception that they take the next number in order to assign them meaning:

da'a su'e su'o za'u me'i
all except n At most n At least n more than n less than n

If no number string follow them, one is assumed.

so'i pa re da'a mu – Many, which is twelve, which is all but five.

The two last number words you should know have slightly more complicated grammar:

ji'i = number rounding or number approximation

When ji'i is placed before a number, the entire number is approximated:

ji'i ze no za'u rau ju'o – "About seventy, which is more than enough, certainly

Placed in the middle of the number, only the following digits are non-exact. At the end of a number, it signifies that the number has been rounded off.

ki'o = Number comma - separates digits within one string; Thousands.

It is not incidential that ki'o sounds like kilo. At its simplest, ki'o is used to separate three digits at a time in large numbers, much like commas are used in English:

pa ki'o so so so ki'o bi xa ze – 1,999,867

If less than three digits are put before a ki'o, the digits are assumed to be the least significant ones, and zeros are assumed to fill in the rest:

vo ki'o ci bi ki'o pa ki'o ki'o – 4,038,001,000,000

ki'o is used similarly after a decimal point.

That concludes the common Lojban numbers themselves. How they apply to sumti is a science in itself, and we leave that for lesson twenty-two. Now we focus on how these numbers can be used in a bridi.

A string of number words by themselves are grammatical, since they can act as an answer to a xo-type of question. In this case, however, they cannot be considered part of any bridi. In general, if numbers fill part of a bridi, they do so in one of two forms: Pure numbers and quantifiers. We will return to quantifiers in a later lesson. For now, we will look at pure numbers.

A pure number is any row of number words prefixed with li. This makes a sumti directly from the number, and refers to the mathematical concept of, for instance, the number six. Its famyma'o is lo'o

li = convert number/mekso-expression to sumti.
lo'o = famyma'o: end convert number/mekso-expression to sumti.

These pure sumti are usually what fills the x2 of brivla such as mitre or cacra

mitre = x1 is x2 metres in dimension x3 by standard x4
cacra = x1 is x2 hours in duration (default 1) by standard x3

Try to translate the following:

le ta nu cinjikca cu cacra li ci ji'i u'i nai

Answer: (sigh) That flirting has been going on for around three hours.

How do you count to three in Lojban?

Answer: li pa li re li ci

The last thing we'll go through in this lesson is the words of the selma'o MAI and those of MOI.

MAI only contains two words, mai and mo'o. Both of these convert any number string to an ordinal, which has the grammar of attitudinals. Ordinals are used to divide a text into numbered segments, like chapters or parts. The only difference between mai and mo'o is that mo'o quantifies larger subdivisions of text, allowing you to divide a text on two different levels, for example enumerating chapters with mo'o and sections with mai. Notice that these as well as the MOI take any number string directly, without any need for li.

mai = Lower-order ordinal marker: Convert number to ordinal.
mo'o = Higher order ordinal marker: Convert number to ordinal.

There are five MOI, and they all convert any number string to selbri. We'll take them one at a time:

moi = Convert number n to selbri: x1 is the n'th member of set x2 by order x3


la lutcimin ci moi lo'i ninmu pendo be mi le su'u lo clani zmadu cu lidne lo clani mleca
Lui-Chi Min is third among my female friends by the order: The more tall ones precedes the less tall ones.

When specifying a sequence, it is widely understood that if a ka-abstraction (lesson thirty) is used as a sumti, the members of the set are ordered from the one with most of the property to the one with less of the property, so the x3 of the following sentence could have been shortened to lo ka clani.

lidne = x1 is before x2 in sequence x3
clani = x1 is long in dimension x2 by standard x3
zmadu = x1 exceeds x2 in property/aspect x3 by amount x4
mleca = x1 is less than/is less characterized than x2 by property/aspect x3 by amount x4
mei = Convert number n to selbri: x1 is the mass formed from the set x2, which has the n members of x3

Notice here that x3 are supposed to be individuals, x2 a set and x1 a mass.

What would mi ci mei mean?

Anwer: We are group of three.

si'e = Convert number n to selbri: x1 is n times x2

Example: le vi plise cu me'i pi pa si'e lei mi cidja be ze'a lo djediThis apple here is less than one tenth of my food for one day

Please note that the definition of si'e when looked up will tell you that it's "x1 is an nth of x2", instead of "x1 is n times x2". But people only use it as I have defined it, so the definition in the dictionaries will probably change.

cu'o = Convert number n to selbri: x1 has n probability of occurring under conditions x2


lo nu mi mrobi'o cu pa cu'o lo nu mi denpa ri
An event of me dying has probability 1 under the conditions: I wait for it = Me dying is completely certain if I wait long enough.
denpa = x1 waits for x2, being in state x3 until resuming/doing x4
va'e = Convert number n to selbri: x1 is at the n'th position on the scale x2


li pa no cu ro va'e la torinon
10 is the highest value on the Torino-scale.

Lesson 20: bo, ke, co, and more cuteness

Say you're an important American buyer of computers. How do you express this? For constructs like these, tanru are ideal: mi vajni merko skami te vecnu. No wait, that's not right. Tanru are grouped from left to right, so this tanru is understood: ((vajni merko) skami) te vecnu, a buyer of computers for important Americans. You can't change the order of the selbri to get a useful tanru. Neither can this be solved with logical connectives, which you will first learn about later anyway. The only way to make a fitting tanru is to force the selbri to group differently.

To bind two selbri close together in a tanru, the word bo can be placed between them: mi vajni bo merko skami bo te vecnu is read mi (vajni bo merko) (skami bo te vecnu), which is useful in this context. If bo is placed between several selbri in a row, they are grouped from right to left instead of the usual left to right: mi vajni merko bo skami bo te vecnu is read vajni (merko bo (skami bo te vecnu)) an important (American computer-buyer), which is even more appropriate in the situation.

bo = Binds two selbri together strongly.

How would you say That's a tasty yellow apple?

kukte = x1 is tasty for x2

Answer: ti kukte pelxu bo plise

What about That's a big, tasty yellow apple?

Answer: ti barda kukte bo pelxu bo plise

Another approach to this is to use the words ke…ke'e. These can be considered as equivalent to the parenthesises used in the paragraph above. ke begins strong selbri grouping, ke'e ends it.

ke = begin strong selbri grouping.
ke'e = end strong selbri grouping.

The strength of the binding is the same as that of bo. Therefore, mi vajni merko bo skami bo te vecnu can be written mi vajni ke merko ke skami te vecnu {ke'e} {ke'e}.

How could you say I'm a German seller of yellow homes?

Answer: mi dotco ke pelxu zdani vecnu

While we're at messing with the ordinary tanru structure, there is another word worth paying attention to. If I want to say that I'm a professional translator, I could say mi fanva se jibri.

jibri = x1 is a job of x2
dotybau = x1 is German used by x2 to say x3
glibau = x1 is English used by x2 to say x3

If I wanted to say that I'm a professional translater from English to German, I'd have to mess around with be and bei: mi fanva be le dotybau bei le glibau be'o se jibri, and the fact that it was a tanru could quickly be lost in speech due to the complicated structure of the sentence. Here, we can use the word co. it inverts the tanru, making the rightmost selbri modify the leftmost instead of the other way around:

mi se jibri co fanva le dotybau le glibau is the same bridi as the previous Lojban one, but much more easy to understand. Notice that any sumti before the tanru fills se jibri, while any following it only fills the modifying selbri: fanva.

co = Invert tanru. Any previous sumti fill the modified, any following fill the modifier.

The strength by which two selbri are bound together with co is very weak – even weaker than normal tanru grouping without any grouping words. This makes sure that, in a co-construct, the leftmost selbri is always the selbri being modified, and the rightmost always modifies, even if any of those parts are tanru. This makes a co-construct easy to parse:

ti pelxu plise co kukte is read ti (pelxu plise) co kukte, which is the same as ti kukte pelxu bo plise. This also means that a ke…ke'e cannot encompass a co.

The cmavo of the selma'o GIhA, the bridi-tail afterthought logical connectives, however, binds even looser than co. This is in order to totally avoid confusion about which selbri binds to which in a GIhA-construct. The answer is simple: The GIhA never emcompasses any selbri-groups.

How can you express I am an important American buyer of computers using a co?

Answer: mi skami te vecnu co vajni merko

If it's of any use, this is the list of different kind of selbri groupers ranked by strength:

  1. bo and ke..ke'e
  2. logical connectives other than bridi-tail afterthought logical connectives (explained in lesson twenty-five)
  3. no grouping words
  4. co
  5. bridi-tail afterthought logical connectives (also in lesson twenty-five)

The rest of this lesson will not be on selbri grouping, but much like lesson seventeen mention assorted words, which can be of use.

bo has another use, which seems separate from selbri grouping: It can also bind a sumtcita to an entire bridi, so that the content of the sumtcita is not a sumti, but the following bridi. This is best explained with an example.

xebni = x1 hates x2

mi darxi do .i mu'i bo mi do xebniI hit you, with motivation that I hate you. Here the bo binds mu'i to the following bridi.

This is where the technical difference between tense sumtcita and other sumtcita is relevant. You see, when binding a normal sumtcita to a bridi with bo, it means that the following bridi somehow fits into the sumti place of the sumtcita. For the reason of God Knows Why, binding one of the words ba or pu to a bridi has the exact opposite effect. For example, in the bridi mi darxi do .i ba bo do cinjikca, one would assume that the second bridi is somehow filled into the sumti place of ba, meaning that the bridi first uttered took place in the future of the second bridi. That's not the case, however, and the correct translation of that utterance would be "I hit you. Afterwards, you flirt". This weird rule is actually one of the main obstacles to a unification of all sumtcita into one single word class. Another difference is that tense-sumtcita can be elided, even though they apply. This rule makes more sense, since we often can assume bridi is placed in a time and space, but we can't assume that the sumtcita of BAI applies.

The unofficial word me'oi is equivalent to me la'e zo'oi, which means that it converts the content of the next word into a selbri. It is used to invent brivla on the fly: mi ca zgana la me'oi X-files for I now watch X-files. Like zo'oi and la'oi, it doesn't allow space, periods (or pauses in speech) inside.

The word gi is strage kind of bridi separator, analogous to .i, but to my knowledge, it is used in only two different kinds of constructs: Most often with logical connectives, explained in lesson twenty-five, but also with sumtcita. With sumtcita it creates a useful, but hardly seen, construct:

mu'i gi BRIDI-1 gi BRIDI-2, which is equivalent to BRIDI-2 .i mu'i bo BRIDI-1. Therefore, the example above, which explained why I hit you, can be written mu'i gi mi xebni do gi mi darxi do, or to preserve the same order as the original sentence, we can convert mu'i with se: se mu'i gi mi darxi do gi mi xebni do.

It is in examples like this that gi really can show its versatility. It does not just separate two bridi like .i does, but can also separate two constructs within a bridi, making all constructs outside the scope of gi apply to both bridi, as this example demonstrates:

cinba = x1 kisses x2 at locus x3

mi ge prami do gi cinba do leaves mi outside the construct, making it apply to both bridi. This can also be done with do, which is also present in broth bridi: mi ge prami gi cinba vau do. Note that vau is needed to make do appear outside the second bridi.

Thus, we can write the original sentence shorter: mi mu'i gi xebni gi darxi vau do, or, to omit even the vau, we can write it even shorter and more elegantly: mi do mu'i gi xebni gi darxi

Lesson 21: COI

In this lesson, you will familiarize yourself with vocatives, or ma'oi coi. They get their own lesson, not because understanding these provides a basis for understanding Lojban grammar in general, or because they are hard to understand, but rather because they are very often used in casual speech, and there are a lot of them.

A vocative is used partly to define who do refers to. If the vocative is followed by a cmevla, the cmevla gets an implied la in front of it. If a selbri follows, a le is used as a gadri instead.

In these examples, I will use the vocative coi, with means Hi or Hello.

If a person is called la + SELBRI, using a vocative with only the selbri to address that person will mean you refer to her as actually being the x1 of that selbri, which is often wrong. If, for instance, a person is called la tsani, Sky, saying coi tsani refers to her as a le tsani, meaning Hi, you sky, while coi la tsani correctly refers to her as someone called "Sky", meaning Hi Sky. This is a frequent mistake, especially among new Lojbanists.

All vocatives have a famyma'o which is sometimes required. This is do'u. It's mostly used if both the first word after the vocative phrase and the last word of the phrase is a selbri, so that it prevents forming a tanru:

do'u = End vocative phrase. Usually elidable.
klaku = x1 cries x2 (tears) for reason x3
coi la gleki do'u klaku fi ma
Hello Happy. Why are you crying?

The generic vocative, doi, does nothing except defining who is being referred to by do:

xu doi .ernsyt. do dotco merko
Ernst, are you a German-American?

All the other vocatives have some content beside defining do. coi, which you know, also means Hello, for example. Many of the vocatives have two or three definitions like the attitudinals. Like attitudinals, this is because they can be modified with cu'i and nai, though only one vocative has the cu'i-form defined.

Some important vocatives are listed in the table below. There are others, but those are not used much.

vocative Without suffix cu'i nai
coi Hello
co'o Goodbye
je'e Understood / OK Not understood
fi'i Welcome Not welcome here
pe'u Please
ki'e Thanks Disappreciation
re'i Ready to recieve Not ready
ju'i Hey! At ease Ignore me
ta'a Interruption
vi'o Will do Will not do
ke'o Please repeat No repeat needed
di'ai well-wish curse

Notice that di'ai is experimental

What would coi co'o mean?

Answer: Greetings in passing or Hello and Goodbye

je'e is used as OK, but also the appropriate response when receiving praise or thanks (at least, if you want to be modest), as it indicates that the praise or thanks was successfully understood.

Translate ki'e sidju be mi bei lo vajni .i je'e .jenifyn.

sidju = x1 helps x2 do x3

Answer: Thanks, you helper of me to do something important. No problem, Jennifer

And fi'i te vecnu .i e'o do citka

Answer: Welcome, buyer. Please eat!

re'i is used to signal that you are ready to be spoken to. It can be used as the Lojban equivalent of What can I do for you? or perhaps replace Hello, when speaking on a phone. re'i nai can mean AFK or Be there is a second.

Translate: Hello, what can I do for you, Interpreter/Translater?

Answer: coi re'i la fanva

ta'a is used when attempting to politely interrupt someone else. What would be good responses to this?

Translate: ta'a ro do mi co'a cliva

cliva = x1 leaves x2 via route x3

Answer: Excuse me for interrupting, everyone. I begin to leave now Notice that no famyma'o or .i is needed.

ke'o is used a lot when inexperienced Lojbanists speak together vocally. It's quite a handy word

sutra = x1 is quick at doing x2

Translate: .y ke'o sutra tavla

Answer: Uh, Please repeat, you quick speaker.

And Okay okay, I got it already! I'll do it!

An answer: ke'o nai .ui nai vi'o

Lesson 22: Quantifying sumti

Most other learning materials such as The Complete Lojban Language and Lojban for Beginners were written before the official adoptation "xorlo", a change in the rules about gadri definition and gadri quantification. The obsoleteness of some of the text in the older learning materials was a major cause for the motivation to write these lessons. Unfortunately for me, quantification of sumti can become a very complex topic when the implications of certain rules are discussed in detail. In order to fulfill the goal of this text being accurate enough to represent the official "gold standard" BPFK rules, this chapter was among the last ones finished and the ones most frequenty rewritten. I strongly encourage anyone who finds mistakes in this text to contact me in order for them to be corrected.

Having said that disclaimer, let's get started:

The first concept you should know about is "distributivity". In lesson fourteen I used the word "individuals" about a group of objects considered distributively. A group of objects considered distributively means that the selbri in question apply to each of the objects. This stands in contrast to non-distributivity (which masses have), in which the group has other properties than each of the individuals do. The distinction between distributivity (individual-like) and non-distributivity (mass-like) is of relevance when quantifying sumti.

Sometimes it's also mentioned how one sumti can distribute over another sumti, so I'll include this as well. What it means is that if sumti A stands in relation X to sumti B, with sumti A distributing over sumti B, then each A stands in relation X to B. Let's have an example in English:

Three dogs bite two men.

If the dogs distribute over the men, then each of three dogs has bitten two men, meaning that between 2 and 6 different men was bitten (since one really unlucky man could have been bitten by all three dogs), whereas if the men distribute over then dogs, then two men were each bitten by tree dogs, fixing the number of men to 2, but allowing between 3 and 6 dogs.

When there can be any doubt as to which sumti distributes over which, the rule is that the first mentioned sumti always distributes over the last mentioned. This is irrespective of place structure, so if x1 and x2 are switched with se, x2, which is mentioned first, will distribute over x1.

Now, back to quantification. Let us first consider how one can quantify description sumti, which are sumti of the form GADRI BRIVLA. The number string which does the quantification can be placed before the gadri, in which case it is referred to as an outer quantifier, and it can be placed between the gadri and the brivla, in which case it's an inner quantifier. Any kind of number string can act as a quantifier.

The rules for how inner and outer quantifiers affects sumti depend on the kind of gadri which is used:

  • lo and le. An inner quantifier tells us how many objects are being spoken of - how many objects are in the discourse total. If an outer quantifier is present, the sumti is distributed over that amount of objects. As stated earlier, if no outer quantifier is present, it's vague how many objects the selbri applies to (though not none), and whether it does so distributively or non-distributively. Examples are always a good idea, so here they are:

mu lo mu bakni cu se jirna - The inner quantifier of five tells us that we speak about five pieces of cattle, and the outer quantifier of five tells us that the selbri is true for each of the five. Therefore, it means "All the five cows had horns".

bakni = x1 is a cow/ox/cattle/calf etc of breed x2
jirna = x1 is the horn of x2 (metaphor: any pointed extremity)

What does the following bridi mean?

lo ru'urgubupu be li re pi ze mu cu jdima lo pa re sovda

ru'urgubupu = x1 is measures to be x2 British pounds (GBP)
jdima = x1 is the price of x2 to buyer x3 set by vendor x4
sovda = x1 is a gamete (egg/sperm) of x2

Answer: "Twelve eggs cost 2.75 British pounds" which, as the English translation, could mean both that they cost 2.75 each (distributively) or that all twelve together cost 2.75 (non-distributively)

so le ta pa pa ci'erkei cu clamau mi (notice that the ta goes before the inner quantifier)

ci'erkei = x1 plays game x2 governed by rules x3 interrelating game parts x4 {this is used to translate "play" in the sense "play a game" rather than, for instance "playing pretend" or "playing House"}
clamau = x1 is taller/longer than x2 in direction x3 my marigin x4

Answer: The inner states there are 11 players in the discourse, and the outer states that the selbri applies to nine of them distributively. Thus it means "Nine of the eleven players are taller than me"

There are a few points that needs to be raised regarding quantification of lo/le:

Using lo with an outer quantifier, "{number} lo {selbri}", works like "{number} {selbri}" in that it quantifies over individuals. Therefore, both ci gerku cu batci re nanmu and ci lo gerku cu batci re lo nanmu consider both the group of dogs and the group of men distributively. Therefore, each of the three dogs bit each of the two men, with six biting events in total.

({number} lo {selbri} is defined as {number} da poi me lo {selbri}, while {number} {selbri} is {number} da poi {selbri}. da and me will be explained later. Put simply, the lo version takes context into account more than the bare number version, which quantifies over anything and everything that fits in the selbri's x1.)

batci = x1 bites/pinches x2 at locus x3 using x4 as pinching tool.

Secondly: What if there is no outer quantifier? Does this mean that it is there, but it's elided? Nope. If there is any kind of outer quantifier, elided or not, it would force the sumti to be distributive, which would mean that neither lo nor le could be used with predicates that apply collectively. Therefore, if no outer quantifier is present, it's not only elided - it's simply not there. Sumti without an outer quantifier can be referred to as "constants".

Thirdly, it makes no sense to have an outer quantifier which is larger than the inner one. It means that the selbri holds true for more sumti than are present in the discourse - but since they appear in a bridi, they are part of the discourse. It's grammatical to do it, though.

Lastly, placing a lo or a le in front of a sumti is grammatical, if there is an inner quantifier present. "lo/le {number} {sumti}" is defined as "lo/le {number} me {sumti}".

So what would this mean? mi nelci lo mi briju kansa .i ku'i ci lo re mu ji'i ri cu lazni

briju = x1 is an office for worker x2 at location x3
kansa = x1 accompanies x2 in action/state/enterprise x3
lazni = x1 is lazy, avoiding work concerning x2

Answer: "I like my co-workers, but three out of about twenty five of them are lazy"

  • la. An inner quantifier is grammatical if the name is a selbri - in this case, it's considered part of the name. An outer quantifier is used to quantify distributively over such individuals (much like lo/le) It's grammatical when placed in front of {number} {sumti}, in which case, the both the number and the sumti is considered the name.

Translate this: re la ci bargu cu jibni le mi zdani

Answer: Two "The Three Arches" are located close to my house" (Perhaps The Three Arches are a kind of restaurant?)

  • loi and lei. An inner quantifier tells us how many members there are in the mass/masses in question. An outer quantifier quantifies distributively {!} over these masses

Notice here that while masses consist of a number of objects considered non-distributively, an outer quantifier always treats each of these masses as an individual.

When placed before a number string, then a sumti, loi/lei is defined as "lo gunma be lo/le {number} {sumti}" - "The mass consisting of the {number} of {sumti}".

Attempt to translate this: dei joi di'e gunma re loi bi valsi .i ca'e dei jai se jalge lo nu jetnu

gunma = x1 is a mass of the individuals x2
valsi = x1 is a word, meaning x2 in language x3
ca'e = Attitudinal: Evidential: I define
jetnu = x1 is true according to metaphysics/epistemology x2

Answer: "This very utterance, mixed together with the next one, forms a mass, consisting of two individual masses each of eight words. I define: This very utterance causes {it} to be true."

  • lai. Much like la, an inner quantifier (when name is a selbri) is part of the name. An outer one quantifies distributively. Before a number+sumti, both the sumti and the number make up the name.

When a fraction is used as an outer quantifier to quantify loi, lei or lai, one speaks about only part of one mass (for instance, "half of the Johnsons" - pi mu lai .djansyn.).

  • lo'i and le'i. An inner quantifier describes the amount of members of the set. An outer quantifies distributively over several of such sets. When placed before a number and a sumti, it's defined as "lo selcmi be lo/le {number} {sumti}" - "The set of {number} {sumti}".

Translate lo'i ro se cinki cu bramau la'a pa no no lo'i ro se bogykamju jutsi

cinki = x1 is an insect of species x2
la'a = Attitudinal: Discursive: Probably
bramau = x1 is bigger than x2 in dimension x3 by marigin x4
bogykamju = x1 is the spine of x2
jutsi = x1 is the species of genus x2, family x3 ... (open ended classification)

Answer: "The set of all the species of insects is probably bigger than one hundred sets of all species of vertebrates"

  • la'i. As with lai

Like with the mass gadri, an outer quantifier before a set gadri enables one to speak about a fraction of a set. In front of a number and a sumti, it's defined as "lo selcmi be la {number} {sumti}" - "The set consisting of The {Number} {Sumti}" (considered a name)

  • lo'e and le'e. Are for some reason not included in the currently accepted gadri proposal. If one were to extend the rules of another gadri, lo/le would probably be the best choice (since both operates with individuals rather than groups), and so one would expect the outer quantifier to force distributivity over the amount of typical/stereotypical things given by the inner quantifier.

When quantifying sumka'i representing several objects, it is useful to remember that they usually behave like lo-sumti. By definition, "{number} {sumti}" is defined as "{number} da poi ke'a me {sumti}". You will not be familiar with da until a few lessons later, so take it on faith that it means "something" in this context. Therefore, ci mi means "Two of those who belong to "us"".

Some important uses of quantification requires you to be quantify selbri or objects whose identity is unknown. This is done by "logically quantified variables". These, as well as how to quantify them will be covered in lessons twenty-seven.

Lastly, how can you quantify uncountable substances like sugar or water? One solution is to quantify it using inexact numbers. This use is vague, not only because the value of the number is vague, but also because it's not specified on what scale you're counting: The sugar could be considered a group of many crystals, counted one at a time, and the water could be quantified by the amounts of raindrops it took to make the body of water in question. While this way of counting is legitimate, it's not very exact and can easily confuse or mislead.

A way to be explicit about non-countability is to use the null operand tu'o as an inner quantifier.

tu'o = Null operand ( Ø ). Used in unary mekso.

This solution is elegant and intuitive, and also gives me an excuse to quote this horrifying, yet comical example from the original xorlo-proposal:

le nanmu cu se snuti .i ja'e bo lo tu'o gerku cu kuspe le klaji

snuti = x1 is an accident on the part of x2
ja'e = sumtcita: BAI: (from jalge): Bridi results in {sumti}
kuspe = x1 spans/extends over x2
klaji = x1 is a road/avenue/street at x2 accessing x3

What does it mean?

Answer: "The man had an accident and so there was dog all over the road"

A second method of quantifying substances is to use the tenses ve'i, ve'a and ve'u as mentioned in lesson ten:

ti ve'i djacu - This is a small amount of water

djacu = x1 is an expanse of water/is made of water/contains water

Thirdly, of course, you could use a brivla to give an exact measurement:

le ta djacu cu ki'ogra be li re pi ki'o ki'o - "That water has a mass of 2.000 000 kilograms"

ki'ogra = x1 measures in mass x2 kilograms by standard x3

Lesson 23: Negation

Sometimes, just saying what's the truth is not enough. Often, we want to specify what's not the truth, and we do this by using negation.

Negation in English mostly involves not, and is completely arbitrary and ambiguous. We, as Lojbanists, can't have that, of course, so Lojban contains an elegant and unambigious system for negating. What will be presented here are the official gold-standard rules. Disapproval of these "golden rules" concerning na is growing, and there is disagreement about what rule set should replace it. For now, I will stick with the official rules, and therefore, so will you, dear reader.

The first you need to know about is bridi negation, so called because it negates the bridi it's in, saying it's not true. The way to negate a bridi is to place na first in the sentence with a ku after it, or just before the selbri.

speni = x1 is married to x2 under convention x3

Thus: na ku le mi speni cu ninmu states that My spouse is not a woman. It states nothing about what my wife is, or if I even have a wife. It only states that I do not have a wife who is also a woman. This has an important implication: If the negation of a bridi is false, the bridi must be true: na ku le mi speni cu na ninmu must mean that I have both a spouse, and that she is a she.

It is possible to use bridi negations in all bridi, even the implicit bridi of descriptive sumti. lo na prenu can refer to anything non-human, whether it be a sphinx, a baseball or the property of appropriateness.

bau = sumtcita, from bangu: using the language of {sumti}
se ja'e = sumtcita, from se jalge: because of {sumti}

Often when using na, it's a problem that it negates the entire bridi. If I say mi na sutra tavla bau le glibau se ja'e le nu mi dotco, I end up negating too much, and it is not clear that I wanted to only negate that I speak fast. The sentence could suggest that I in fact speak fast because of some other reason, for instance that I speak fast in French because I'm German. To express the sentence more precisely, I need to only negate that I speak fast, and not the other things.

To only negate part of a bridi, na ku can be moved around the bridi and placed anywhere a sumti can go. It then negates any sumti, selbri and sumtcita placed after it. When placed immediately before the selbri, the ku can be elided.

Moving na ku from the left end of the bridi and rightwards effects any quantifiers in a certain way, as can be seen by this example:

There are forces within the Lojban community who, perhaps rightly, think that there is no good reason that a na placed before a selbri negates the entire bridi, whereas a na ku any other place negates only what is trailing behind it. However, in these lessons you will be taught what is still the official stance, namely that na before the selbri negates the bridi.

The use of na ku is exemplified with the following examples.

na ku ro remna cu verba It's not true that: All humans are children

su'o remna na ku cu verba For at least one human it's not true that: It's a child. See that the na ku is placed before cu, since a sumti can go only before, not after the cu. Had I only used na, it would have to go after cu - but that would have negated the entire bridi, meaning "It's not true that: At least one human is a child".

When the na ku is moved rightwards, any quantifier is inverted - that is: ro is turned into su'o. This is, of course, only if the meaning of the bridi has to be preserved. This means that when the na ku is placed at the end of the bridi, only the selbri is negated but all the sumti and sumtcita are preserved, as can be seen by these three identical bridi:

ckule = x1 is a school at location x2 teaching x3 to students x4 and operated by x5

na ku ro verba cu ve ckule fo su'o ckuleIt's not true that all children are students in a school.

su'o verba cu ve ckule na ku fo su'o ckuleSome children are students in not a single school.

su'o verba cu ve ckule fo ro ckule na kuSome children are for all schools not students in them.

The opposite of na is ja'a. This is barely ever used, since it is default in most bridi. One exception is repeated bridi (next lesson). Sometimes it's used to put more weight on the truth of the bridi, as in la .bab. ja'a melbi = "Bob is indeed beautiful".

While the mechanism of na ku resembles natural language negation, it can be difficult to keep track of exactly what is negated and how that affects the bridi. For that reason, the construct na ku is rarely seen anywhere other than the beginning of a bridi. In most cases where more specific negation is needed people resort to a different method. This method, called scalar negation, is an elegant and intuitive tool. Using it, you effect only the selbri, since the words used in scalar negation binds to the selbri much like the word se.

The name scalar negation is derived from the fact that the words which bind to the selbri can be placed along a scale from affirmation over negation and to stating that the opposite case is true:

These words are not negators in the same sense as na. They do not state that a bridi is false, but makes a positive statement that a bridi is true – the same bridi, but with a different selbri. This distinction is mostly academic, though. If, for example, I state that mi na'e se nelci "I am non-liked", I actually state that some selbri applies to me, which is also on a relevant scale with the selbri nelci. Most of the time, we assume a scale where the positions are mutually exclusive (like love-like-dislike-hate), so mi na'e se nelci implies mi na se nelci Therefore, the words no'e and to'e should only be used when the selbri is placed on some obvious scale: le mi speni cu to'e melbiMy spouse is ugly makes sense, since we immediately know what the opposite of beautiful is, while mi klama le mi to'e zdaniI go to my opposite thing of home, while grammatical, leaves the listener guessing what the speaker's opposite-home is and should be avoided. So how can you negate only the selbri without also implying that the selbri is correct at some other position on a truth-scale? Simple: Moving the na ku to the rightmost end of the bridi, as demonstrated a few lines above. This feature is very useful. Some Lojbanists prefer to prefix the rafsi nar (the rafsi of na) in front of the selbri - this has the same effect, but I advise against it, because it makes familiar brivla seem alien, and it's harder to understand when spoken casually. If a situation arises where you need to negate only the selbri, but want it to be clear before the end of the bridi, the experimental cmavo na'ei, which grammatically works like na'e, can be used na'ei: Negates the following selbri only Try to translate these sentences: My spouse is not a woman (meaning that he is a male) Answer: le mi speni cu na'e / to'e ninmu. Using scalar negation here implies that he exists, which na did not.My spouse is not really a woman Answer: le mi speni cu no'e ninmu. The scale here is presumed to be from woman to man.I don't speak fast in English because I'm German Answer: mi na'e sutra tavla bau le glibau se ja'e le nu mi dotco Also, note that whenever these words are used together with a tanru, they only affect the leftmost selbri. In order to make it bind to the whole tanru or parts of the tanru, the usual tanru-grouping words can be used. Try to say I sell something which is not yellow homes using the tanru pelxu zdani vecnu Answer: mi na'e ke pelxu zdani ke'e vecnu or mi na'e pelxu bo zdani vecnu When attempting to answer: Is the king of the USA fat?, all of these negations fail. While it's technically correct to negate it with na, since it makes no assumptions of that is true, it's mildly misleading since it could lead the listener to believe there is a king of the USA. For these scenarios, there is a metalinguistic negator, na'i.
na'i = metalinguistic negator. Something is wrong with assigning a truth value to the bridi.
Because na'i can be needed anywhere it has been given the grammar of the attitudinals, which means it can appear anywhere, and it attaches to the previous word or construct.
palci = x1 is evil by standard x2
le na'i pu te zukte be le skami cu palci
The sought goal {mistake!} of the computer was evil, probably protests that computers can seek a goal volitionally.

Since this is a lesson on negation, I believe the word nai deserves a short mention. It is used to negate minor grammatical constructs, and can be used in combination with attitudinals, all sumtcita including tenses, vocatives and logical connectives. The rules for negating using nai depend on the construct, and so the effect of nai has been discussed when mentioning the construct themselves. The exception is sumtcita, where the rules for negation are more complex, and will not be discussed here.

Note: At the time of writing, it has been proposed to move nai to the selma'o CAI, which means the semantics of nai depend on which selma'o it follows.

Lesson 24: brika'i/pro-bridi and ko'a

If I say that I'm called Mikhail, zo .mikail. cmene mi, and you have to say the exact same bridi, what would that be? One of the many answers is do se cmene zo .mikail.. For the bridi to be the same, you have to replace mi with do, and it doesn't matter which if you say the bridi with the se-converted selbri or not. This is because a bridi is not the words which express it – a bridi is an idea, an abstract proposition. The word mi when I say it and the word do when you do refers to the same sumti, so the two bridi are identical.

This lesson is on brika'i, the bridi equivalent of sumka'i. They are word which represent entire bridi. Here it is important to remember that a bridi consists only of sumti and the things which contain the sumti, selbri and sumtcita. Neither attitudinals, nor the semantic layer of ko or ma are part of the bridi proper, and so these are not represented by a brika'i.

There are much fewer brika'i than there are sumka'i. We will begin by going through some of the words in the most used series, called GOhA:

go'u = Repeats remote past bridi
go'a = Repeats past bridi
go'e = Repeats next-to-last bridi
go'i = Repeats last mentioned bridi
go'o = Repeats future bridi
nei = Repeats current bridi
no'a = Repeats outer bridi

Some of the GOhA-brika'i. Notice the familiar i, a, u-pattern for close in past, medium in past and distant in past.

These are very much like the sumka'i ri, ra and ru. They can only refer to main bridi of jufra, and not those contained in relative phrases or description sumti. The main bridi can contain a relative phrase, of course, but a brika'i can never be used to refer to only the relative phrase.

A GOhA acts grammatically much like a selbri, any construct which can apply to selbri can also apply to these. The place structure of a GOhA is the same as that of the bridi it represents, and the sumti are by default the same as in the bridi it represents. Filling the sumti places of a GOhA explicitly overwrites the sumti of the bridi it represents. Contrast:

A: mi citka lo plise B: go'iI eat an apple. You do. with

A: mi citka lo plise B: mi go'iI eat an apple. I do, too.

These brika'i are very useful when answering a question with xu:

A: xu do nelci le mi speni B: go'i / na go'iDo you like my wife? Yes./No.. The xu, being an attitudinal, is not copied.

When repeating bridi negated by na, that is: Bridi where na is placed in the prenex (lesson twenty-seven), in the beginning of the bridi or right before the selbri, the rules for copying over na are different from what one might expect. Any na is copied over, but any additional na in the brika'i replaces the first na. Let me show you with an example:

A: mi na citka lo plise

B: mi go'i = mi na citka lo plise

C: mi na go'i = mi na citka lo plise

D: mi na na go'i = mi citka lo plise = mi ja'a go'i

nei and no'a are not used much, except for mind-breaking purposes, which is making up bridi which are hard to parse, like dei na se du'u le no'a la'e le nei. Since nei repeats the current outer bridi, however, le nei can be used to refer to the x1 of the current outer bridi, le se nei the x2 and so on.

When using brika'i, one must always be wary of copying sentences with the personal sumka'i like mi, do, ma'a ect, and be careful not to repeat them when they are in the wrong contect, as shown in the two examples with apple eating above. Instead of replacing them one by one, though, the word ra'o anywhere in the bridi updates the personal sumka'i so that they apply for the speaker's perspective:

A: mi do prami B: mi do go'i is equivalent to A: mi do prami B: go'i ra'o

ra'o = Update all personal sumka'i so that they now fit the speaker's point of view.

The only other series of brika'i are very easy to remember:

broda = Bridi variable 1
brode = Bridi variable 2
brodi = Bridi variable 3
brodo = Bridi variable 4
brodu = Bridi variable 5
cei = Define bridi variable (not a brika'i and not in BRODA)

The first five are just five instances of the same word. They can be used as shortcuts to bridi. After saying a bridi, saying cei broda defines that bridi as broda, and broda can then be used as brika'i for that bridi in the following conversation.

While we're at it, there is an analogous series of sumka'i, which probably does not belong in this lesson, but here they are anyway:

ko'a Sumti variable 1 fo'a Sumti variable 6
ko'e Sumti variable 2 fo'e Sumti variable 7
ko'i Sumti variable 3 fo'i Sumti variable 8
ko'o Sumti variable 4 fo'o Sumti variable 9
ko'u Sumti variable 5 fo'u Sumti variable 10

as well as the cei-equivalent for this series:

goi = Define sumti variable

These are used like the brika'i-series. Just place, for instance, goi ko'u after a sumti, and that sumti can be referred to by ko'u.

Strangely, these series are rarely used for their intended purpose. They are, however, used as arbitrary selbri and sumti in example texts, where broda and brode mean "any selbri A" and "any selbri B" and similarly for ko'a and friends:

So, is it true that the truth conditions of ko'a ko'e broda na ku are always the same as na ku ko'a ko'e broda? Nope, it isn't.

Lesson 25: Logical connectives

If you ask a Lojbanist: Do you want milk or sugar in your coffee? she'll answer: Correct.

Witty as this joke might be, it illustrates a weird property of the English way of asking this question. It is phrased as a true/false question, but it really isn't. In Lojban, we can't have this kind of inconsistency, and so we must find another way of asking this kind of question. If you think about it, it's pretty hard to find a good and easy way, and it seems Lojban have picked a good way instead of an easy way.

To explain it, let us take two separate bridi: Bridi 1: I like milk in my coffee and bridi 2: I like sugar in my coffee. Both of these bridi can have the state true or false. This yields four combinations of which bridi is/are true:

A ) 1 and 2 B ) 1 but not 2

C ) 2 but not 1 D )neither 1 nor 2

I, in actuality, like milk in my coffee, and I'm indifferent as to whether there is sugar in it or not. Therefore, my preference can be written A ) true B ) true C ) false D ) false, since both A and B yields true for me, but neither C nor D does. A more compact way of writing my coffee preferences would be TTFF for true, true, false, false. Similarly, a person liking his coffee black and unsweetened would have a coffee preference of FFFT. This combitation of "true" and "false" is called a truth function, in this case for the two statements I like milk in my coffee and I like sugar in my coffee. Note that the order of the statements matters.

In Lojban, we operate with 4 truth functions, which we consider fundamental:

A: TTTF (and/or)

O: TFFT (if and only iff)

U: TTFF (whether or not)

E: TFFF (and)

In this example, they would translate to something like: A:Just not black coffee, O: Either both milk or sugar, or nothing for me, please, U: Milk, and I don't care about if there's sugar or not and E: Milk and sugar, please..

In Lojban, you place the word for the truth function between the two bridi, selbri or sumti in question. That word is called a logical connective. The words for truth functions between sumti (and just for sumti!) are .a .o .u and .e. How nice. For instance: I am friends with an American and a German would be lo merko .e lo dotco cu pendo mi.

How would you say: I speak to you and no one else?

Answer: mi tavla do .e no drata Note that this actually states that it's true that "I speak to you".

One more: I like cheese whether or not I like coffee

ckafi = x1 is a quantity/contains coffee from source/of grain x2

Answer: mi nelci lo'e cirla .u lo'e ckafi

You can perhaps deduce that there are sixteen possible truth functions, so we need to learn twelve more in order to know them all. Eight more can be obtained by negating either the first sentence or the second. The first is negated by prefixing the truth function word with na, the second is negated by placing nai after the word. For example, since .e represents TFFF, .e nai must be both 1 is true and 2 is false, which is FTFF. Similarly, na .a is Just not: 1 is true and 2 is false, which is TTFT. Doing this type of conversion in the head real-time is very, very hard, so perhaps one should focus on learning how logical connectives work in general, and then learn the logical connectives themselves by heart.

Four functions cannot be made this way: TTTT, TFTF, FTFT and FFFF. The first and the last cannot be made using logical connectives at all, but they are kind of useless anyway. Using a hypothetical logical connective in the sentence I like milk FFFF sugar in my coffee is equivalent to saying I don't like coffee, just more complicated. The last two, TFTF and FTFT, can be made by prefixing .u with good ol' se, which just reverts the two statements. se .u , for instance is B whether or not A, which is TFTF. The final list of all logical connectives can be seen below.

TTTT: Cannot be made

TTTF: .a

TTFT: .a nai

TTFF: .u OR .u nai

TFTT: na .a

TFTF: se .u

TFFT: .o OR na .o nai

TFFF: .e

FTTT: na .a nai

FTTF: na .o OR .o nai

FTFT: se .u nai

FTFF: .e nai

FFTT: na .u OR na .u nai

FFTF: na .e

FFFT: na .e nai

FFFF: Cannot be made

Logically, saying a sentence with a logical connective, like for instance mi nelci lo'e cirla .e nai lo'e ckafi is equivalent to saying two bridi, which are connected with the same logical connective: mi nelci lo'e cirla .i {E NAI} mi nelci lo'e ckafi. This is how the function of logical connectives is defined. We will get to how to apply logical connectives to bridi in a moment.

By putting a j in front of the core word of a logical connective, it connects two selbri. An example is mi ninmu na jo nanmu I am a man or a woman, but not both

ninmu = x1 is a woman

This is tanru-internal, meaning that it loosely binds selbri together, even when they form a tanru: lo dotco ja merko prenu means a German or American man, and is parsed lo (dotco ja merko) prenu. This binding is slightly stronger that normal tanru-grouping (still weaker than specific grouping-words), and as such, lo dotco ja merko ninmu ja nanmu is parsed lo (dotco ja merko) (ninmu ja nanmu). The selbri logical connectives can also be attached to .i in order to connect two sentences together: la .kim. cmene mi .i ju mi nanmu I'm called Kim, whether or not I'm a man. The combination .i je states that both sentences are true, much like we would assume had no logical connective been present.

Unfairly hard question: Using logical connectives, how would you translate If you're called Bob, you're a man.?

Answer: zo .bab. cmene do .i na ja do nanmu or Either you're not named Bob and a man, or you're not named Bob and not a man, or you're named Bob and a man. But you can't be named Bob and not be a man. The only combination not permitted is: You're called Bob, but not a man. This must mean that, if it's true that you're called Bob, you must be a man.

If we try to translate the sad, sad event of I cried and gave away my dog, we run into a problem.

Attempting to say the sentence with a je between the selbri gave and cried, would mean the same word for word, but unfortunately mean that I cried the dog and gave away the dog, cf. the definition of logical connectives. One can cry tears or even blood, but crying dogs is just silly.

However, we can get around by using bridi-tail logical connectives. What they do is that any previous sumtcita and sumti attaches to both selbri bound by the bridi-tail logical connective, but any following sumti or sumtcita only applies to the last mentioned: The bridi splits up from one head to two tails, to speak metaphorically.

The form of a bridi-tail logical connective is gi'V, with the V for the vowel of the truth function.

How could you correctly translate the English sentence to Lojban?

Answer: mi pu klaku gi'e dunda le mi gerku

What does ro remna cu palci gi'o zukte lo palci mean?

palci = x1 is evil by standard x2

Answer: People are evil if and only if they do evil things.

Furthermore, there is a forethought all-but tanru internal group of connecters made by prefixing g in front of the truth function vowel. Forethought in this context means that they need to go in front of the things they connect, and thus you need to think about the grammatical structure of the sentence before saying it. All-but tanru internal means that it serves both as a connective between sumti, bridi, selbri and bridi-tails, but not between two selbri of one tanru. Let me show you how it works, rewriting the Lojban sentence above:

go lo remna cu palci gi lo remna cu zukte lo palci

The first logical connective in these kinds of constructs are what carries the vowel which signal what truth function is being used. The second logical connective is always gi, and like .i, it has no truth function. It simply serves to separate the two terms being connected. If you want to negate the first or second sentence, a nai is suffixed to either the first (for the first sentence) or second (for the second sentence) logical connective.

Provided that the constructs are terminated properly, it has remarkable flexibility, as the following few examples demonstrate:

mi go klama gi cadzu vau le mi zdani I go, if and only if walk, to my home or I can only go to my home by walking. Notice that the vau is needed to make le mi zdani apply to both cadzu and klama.

se gu do gi nai mi bajra le do ckule Whether or not you, then not I, run to your school or I won't run to your school no matter if you do or not

The tanru-internal equivalent of gV is gu'V. These are exactly the same, except that they are exclusively tanru-internal, and that they bind a selbri to the gi tighter than normal tanru-grouping, but weaker than explicit binding-sumti:

la xanz.krt. gu'e merko gi dotco nanmu is equivalent to

la xanz.krt. merko je dotco nanmu

And so you've read page up and page down just to get the necessary knowledge in order to be able to learn how to ask Would you like milk or sugar in your coffee? in Lojban. Simply place a question logical connective instead of another logical connective, and like ma, it asks the listener to fill in a correct response. Unfortunately, these question-logical connectives don't always match the morphological pattern of the logical connectives they ask for:

ji = Logical connective question: Asks for a sumti logical connective (A)
je'i = Logical connective question: Asks for a tanru-internal selbri logical connective (JA)
gi'i = Logical connective question: Asks for a bridi-tail logical connective (GIhA)
ge'i = Logical connective question: Asks for a forethought all-but tanru internal logical connective (GA)
gu'i = Logical connective question: Asks for a forethought only tanru internal logical connective (GUhA)

So... how would you ask if the persons wants milk or sugar in her coffee?

ladru = x1 is/contains milk from source x2
sakta = x1 is/contains sugar from source x2 of composition x3

Possible answer: sakta je'i ladru le do ckafi though I guess something more English and less elegant could also suffice like do djica lenu lo sakta ji lo ladru cu nenri le do ckafi

Lesson 26: Non-logical connectives

The word "logical" in "logical connective" refers to the association a logical connective has with a truth function. Not all useful connectives can be defined through a truth function, however, and so there are other connectives beside the logical ones.

The meaning of a logical connective is defined the same as two different bridi connected with that logical connective. For instance, mi nitcu do .a la .djan. is defined to be equivalent to mi nitcu do .i ja mi nitcu la .djan.. This definition is useful to bear in mind, because it implies that sometimes, sumti cannot be connected with logical connectives without chaning the meaning. Consider the sentence: "Jack and Joe wrote this play." One attempt at a translation would be: ti draci fi la .djak. e la .djous.

draci = x1 is a drama/play about x2 by writer/dramatist x3 for audience x4 with actors x5

The problem with this translation is that it means ti draci la .djak. ije ti draci la .djous., which is not really true. Neither Jack nor Joe wrote it, they did so together. What we want here is of course a mass, and some way to join Jack and Joe in one mass. This has little to do with a truth function so we must use a non-logical connective, which are of selma'o JOI. We'll return to this Jack and Joe-problem in a little - first: Four of the known JOI:

The Lojban connective joins sumti and forms a:

The functions of these words are simple: lo'i remna jo'u lo'i gerku considers both the set of humans and the set of dogs distributively (as individuals). Remember from lesson twenty-two (quantifiers) that "distributivity" means that what is true for the group is also true for each of the individuals alone. Similarly loi ro gismu ce'o loi ro lujvo ce'o loi ro fu'ivla is a sequence consisting of the mass of all gismu, followed by the mass of all lujvo, followed by the mass of all fu'ivla. As with all of the JOI which has an inherent order, se may be put before ce'o to inverse the order: "A ce'o B" is the same as "B se ce'o A". How can you correctly translate "Jack and Joe wrote this play"? Answer: ti draci fi la .djak. joi la .djous. The cmavo of JOI are very flexible: They can act both as sumti connectives and tanru-internal connectives, so they can be used to connect sumti, selbri and bridi. This flexibility means that one must be careful to use famyma'o correctly when using a JOI. What is wrong with the bridi lo dotco jo'u mi cu klama la dotco gugde? Answer: jo'u is put after a selbri, so it expects a selbri after it to connect to, but none is found. Had a ku been present before the connective, it would have been grammatical If several JOI are used, bo and/or ke may be used to override the usual left-grouping:
mi joi do ce'o la .djak. joi bo la .djous. cu pu'o ci'erkei damba lei xunre
Me and you, and then Jack and Joe are about the play against the reds

Contrast it with

mi joi do ce'o la .djak. joi la .djous. cu pu'o ci'erkei damba lei xunre
First me and you, then Jack will together with Joe play against the reds.

Connecting bridi with JOI can make some interesting implications of the relationship between the bridi:

la .djak. morsi ri'a lo nu ri dzusoi .i joi le jemja'a po ri cu bebna
Jack is dead because he was a infantry soldier and his general was an idiot.

implying that these two bridi massed together was the physical cause of his death: Had he only been in an armored vehicle or with a competent commander, he might had survived.

dzusoi = x1 is an infantry soldier of army x2
jemja'a = x1 is a general of army x2 in function x3
bebna = x1 is foolish/idiotic in property/aspect x2

Non-logical connectives may also be negated with nai, indicating that some other connective is appropriate: lo djacu ce'o nai .e'o lo ladru cu cavyfle fi le mi tcati - "Please don't pour first water then milk in my tea". This, of course, says nothing about which connective is appropriate - one might guess se ce'o (first milk, then water), only to find out that .e nai (only water, no milk at all) was the correct one.

cavyfle = x1, consisting of x2, flows into x3 from x4

Just like a logical connective is a plausible negation of a non-logical connective, answers to questions of the type ji or je'i can be both logical and non-logical: A: ladru je'i sakta le do ckafi B: se ce'o ("Milk or sugar in you coffee?" "First the latter, then the former"). In this case ce would make no sense at all, since sets can't be contained in coffee, and joi (both mixed together) would mean the same as jo'u (both of them), unless the respondant preferred unmixed sugar in his coffee.

The fifth JOI I present here is a bit of an oddball:

fa'u = Non-logical connective: Unmixed ordered distribution (A and B, respectively)

When only one fa'u is placed within a bridi (or several bridi connected together with connectors), fa'u may be assumed to be identical to jo'u. When several fa'u is used within one bridi, however, the constructs before fa'u each apply to each other, and the constructs after fa'u each apply to each other. Let's have an example:

mi fa'u do rusko fa'u kadno
You and I are Russian and Canadian

implying that mi goes with rusko and do goes with kadno, and implying nothing about any other combination. Of course, in this example, it would be much easier to say mi rusko .i do kadno.

These last three JOI connects two sets to make new sets:

jo'e = A union B
ku'a = A intersection B
pi'u = Cross product of A and B

These are probably not very useful for the average Lojbanist, but I might as well include them here.

The first one, jo'e, contains all the members of set A and those of set B. If anything is a member of both sets, they are not counted twice.

A set made with ku'a makes a new set from two sets. This new set contains only those members which are in both sets.

pi'u is a little more complicated. A set "A pi'u B" contains all the possible combinations of "a ce'o b", where a is a member of A and b is a member of B. It is thus a set of sequences of members. If, for instance, set A contained the members p and q, and set B contained members f and g, then A pi'u B would be a set consisting of the four members p ce'o f, p ce'o g, q ce'o f and q ce'o g.

Lesson 27: Lojban logicː da, bu'a, zo'u, and terms

Here we are starting to talk about advanced Lojban. The Lojban in this and following lessons is rarely relevant when speaking Lojban in normal contexts, but it pops up quite often when speaking about language and logic.

These corners of Lojban is for the most part experimental, new or complex, so you should expect a lot of changing definitions, outdated definitions, disagreements and misunderstandings on the part of the author of this text. Sorry about that.

The stated topic of this lesson needs some justification: This lesson is not really about how do to logic in Lojban, since firstly, logic is presumably the same in all languages, and secondly, actually teaching logic would be totally impractical in one single lesson. Rather, this lesson explains some constructs which resemble those which logicians use. It turns out they have a remarkable wide range of uses in Lojban.

Getting involved in the more obscure details of these logical constructs can be mind-warpingly difficult, and there will always be some disagreement in the corners of this part of the language.

Learning these logical constructs requires one to learn a bit about constructs which are not logical in nature. Let's begin with zo'u

zo'u = Separates prenex from bridi

Before any zo'u is the prenex, after zo'u is the bridi. Informally, a prenex is a place in front of the bridi, where you put a bunch of terms. A term is an English word given to some kinds of Lojban constructs: Sumti, sumtcita with or without sumti attached, na ku and an abomination called termsets, which I refuse to include in these lessons. The prenex is not part of the bridi, but any terms put inside it gives us information about the bridi. One can, for example, use it to state a topic as shown thus:

lo pampe'o je nai speni zo'u mi na zanru - "Concerning lovers who are not spouses: I do not approve". The benefits of kind of sentence structuring is questionable, but it's always good to have some variation to play with. Furthermore, constructing sentences this way resembles Mandarin (and other languages) closely, meaning it might seem more intuitive for speakers of that language.

pampe'o = x1 is a lover of x2
zanru = x1 approves of x2 (plan, event or action)

Of course, the relation between the terms in the prenex and the bridi is vague. One can imagine any sumti in the prenex bearing the same relevance to the bridi as if they were put in the bridi after a do'e sumtcita, and any sumtcita in the prenex doing pretty much the same as if they were in the bridi. It is quite possible to put terms in prenexes without any clear hints as to how the term may relate to the bridi:

le vi gerku zo'u mi to'e nelci lo cidjrpitsa - "Concerning this dog here: I dislike pizza." It leaves you guessing about the reason for mentioning the dog.

cidjrpitsa = x1 is pizza with topping/ingredients x2

If the prenex contains na ku, it's pretty straight forward: The entire bridi is negated, just as if the bridi itself began with na ku.

So how long does a prenex last? It lasts until the following bridi is terminated. If that is not desired, there are two ways to make it apply to several bridi: One is to put some kind of connective after the .i separating the bridi, and another method is to simply include all of the text in tu'e ... tu'u-brackets. These brackets work pretty much by gluing all the bridi together and makes all sorts of construct apply to several bridi.

Now that we covered zo'u, the first "logical" words we can use it with are these:

da = logically quantified existential sumka'i 1
de = logically quantified existential sumka'i 2
di = logically quantified existential sumka'i 3

These words are all the same, like the mathematical variables x, y and z. Once you have defined them, however, they keep refering to the same thing. These words are defined in the prenex of bridi, meaning that when the prenex stop applying, the definition of these three words are cancelled.

The words da, de and di can refer to literally any sumti, which makes them kind of useless unless restricted in some way. The first and foremost way to restrict them is to quantify them: They are not called "logically quantified existential sumka'i" for nothing. They are sumka'i, they are most useful when quantified, and they are existential. What does it mean, being "existential"? It means that by default, they are used to assert that something exists. An example:

The statement pa da zo'u da gerku has pa da in the prenex, which means "There exists one thing such that it:", and then da, now defined, is used in the bridi da gerku. Translated to English, this means: "There exists one thing which is a dog". This is obviously false, there are around 400,000,000 of them in the world. If da and its sisters are not quantified, the number su'o is the default. Thus da zo'u da gerku means "There exist at least one thing which is a dog", which is true. Notice here, that any quantification must be more or less exact in order to be true: Of course one dog exists, but in Lojban, pa da zo'u da gerku means not only that does one dog exists, but also that no more than one does.

There are a few specific rules to these existential sumka'i:

- If the quantifier ro is used before da, it instead refers to "all which exists".

- Importantly, the usage of an existential sumka'i only asserts that such a thing exists in the domain of truth where it's used. Thus, in the sentence so'e verba cu krici lo du'u su'o da crida, does not state da crida, since its "domain of truth" is only inside the du'u-abstraction. Generally speaking, abstractions contain their own domain of truth, so using da and friends inside an abstraction is usually safe.

- If the same variable is quantified several times, the first quantification is the one which sticks: Any later quantified instance of that variable can refer only to things which are also being referred to by the first instance of that variable, and any later non-quantified instance of that variable will gain the first quantifier. To use an example: ci da zo'u re da barda .ije da pelxu means "There exists three things such that two of them are big and all three are yellow". re da, being after ci da, can only refer to two of the already stated three things. When da appears without a quantifier, ci is assumed.

- If there are several terms in the prenex, the terms are always read left to right. Sometimes, this matters: ro da de zo'u da prami de means "Concerning all the things X that exists, concerning at least one thing Y: X loves Y". This is the same as "All things love at least one thing.", where the "thing(s)" can be anything, including the thing itself. Note here that de can refer to different things for each da - the thing which is referred to by de is dependent on the da, since it came before it in the prenex, therefore each thing might love something different. If we switched the places of da and de in the prenex, a different result would arise: de ro da zo'u da prami de = "Concerning at least one thing Y, concerning all X which exists: X loves Y", meaning "There exists at least one thing which everything loves".

Of course, both claims are completely false. There are many things which loves nothing - rocks, or abstract concepts, for example. Likewise, it's impossible to concieve of something which everything loves, since "everything" also encompasses non-sentient things. We need better ways to restrict what these variables can point to. One good way of doing it is to make them the subject of a relative clause:

ro di poi remna zo'u birka di = "Concerning all X that exists, which is human: X has one or more arms." or "All humans have arms", which is true, at least when speaking in a potential, timeless sense.

birka = x1 is an arm of x2

When restricting claims using this kind of logical "existential" variable, it's very important to remember that unless there is an explicit no or ro as a quantifier, these kind of statements always imply that there actually exists something which can be referred to by da. Therefore, any kind of non-negated statement where da points to something which does not exist is false.

ro da was also originally defined to imply existence, but is now usually taken to be equivalent to no da naku, "nothing exists that does not ...". Having this equivalence hold no matter what the formula evaluates to is seen as more important than having {ro} mirror natural language use exactly.

In fact, you don't really need the prenex to define the variables. You can use them directly as sumti in the bridi, and quantify them there. You only need to quantify them the first time they appear, though. Thus, the sentence about humans having arms could be turned into birka ro di poi remna. The order of the variables still matters though, and so the prenex can be used to avoid having to mess up your bridi to place the variables in the correct order. When having more variables, a prenex is usually a good idea.

The second kind of logical words are basically the same as the three we have already been though, but these are brika'i instead of sumka'i:

bu'a = logically quantified existential brika'i 1
bu'e = logically quantified existential brika'i 2
bu'i = logically quantified existential brika'i 3

These work pretty much the same way as the other three, but there are a few points which are important to mention:

Since only terms can go in the prenex, these brika'i need to have a quantifier in order to make them into sumti. When quantified in the prenex, however, the quantifier works very different from quantifiers with normal selbri: Instead of quantifying the amount of things which fits the x1 of the selbri variable, it directly quantifies the amount of selbri which applies. Again, the default quantifier is so'u. Thus, instead of re bu'a zo'u meaning "Concerning two things which is in relationship X:", it means "Concerning two relationships X:"

It's probably good to see an example of bu'a put to practice:

ro da bu'a la .bab. = "Considering all X which exists: X is in at least one relationship with Bob" = "Everything is related to Bob in at least one way.". Notice again the order matters: su'o bu'a ro da zo'u da bu'a la .bab. means: "There is at least one relationship such that everything that exists is in that relationship with Bob". The first statement is true - for any one thing, one can indeed make up some selbri which relates any guy called Bob and it. But I'm not sure the latter is true - that one can make a selbri which can relate anything, no matter what it is, and Bob.

Let's have an example which quantifies selbri:

ci'i bu'e zo'u mi bu'e do - "Concerning an infinite amount of relationships: I am in all those relationship with you." or "There exists an infinite amount of relationships between us"

You can't quantify the selbri variables in the bridi itself, though. Then it will act as a sumti: mi ci'i bu'a do is not a bridi. There are some situation where this will become problematic - lesson twenty-nine will teach how to overcome those problems.

Lesson 28: Types

This lesson along with the following three lessons will be on semantics - how to interpret the meaning of certain constructs. This lesson is on the meaning of different types of sumti, and will get philosophical and a bit hazy. The following two will be on abstractions, which, even though you already became familiar with them twenty-two lessons ago, will become more technical as I attempt to explain their semantic and grammatical properties.

Teaching (and learning) semantics is much more tricky than teaching grammar, especially in Lojban, where grammar is black-or-white, but semantics isn't. Therefore, I find it necessary to repeat an earlier disclaimer the following is not official, but rather an (educated) opinion on the language.

Bad grammar is easy to spot in Lojban - in fact it's unambiguously correct or not. In contrast, saying that a jufra is semantically wrong is the same as saying that the speaker is using Lojban to think wrongly about the world. It's not saying "You can't say X" as much as "You can't interpret X in this way. You should interpret it this way". Placing these restrictions on composing and understanding language is a slippery slope leading to restrictions on creativity, and even presupposing of certain metaphysical viewpoints while excluding others.

Then why include semantic standards in a textbook? Shouldn't any speaker be free to say anything, and any listener be free to let that speech mean whatever they want?

This is a matter of measure. Given that extreme, that is, if no semantic standards were set, everything could mean anything, and all communication would be meaningless. In any language which aims to facilitate communication, one must be able to express oneself in such a way that one can trust that one’s message is interpreted in the desired way. Semantic rules of Lojban do not exist in order to prevent people from saying A. They exist to prevent people from saying B and having others think they meant A.

This lesson is on types. The word type, informally translated to klesi, is used by Lojbanists to describe the existential nature of the things sumti describe. This nature is, and must be, the same as the nature of the things described by other languages such as English. However, in Lojban, the different ways of making sumti denote which type a sumti belongs to, so while the exact natures of sumti can be ignored in English, Lojbanists have to deal with them.

When speaking of types, Lojbanists often mention what type a sumti really is. When beginning from the beginning, we have to remember that this certainty is not philosophically well grounded. Taking a materialistic viewpoint, the natural world of particles and waves does not correspond well with human understanding of say, hatred, which is not defined by any specific particles, nor any specific brain activity. It is a purely abstract concept. Similarly, in an extreme inductionist viewpoint, such as that taken by Hume, all we humans experience are subjective impressions over time - a long string of events, or, some people argue, a bunch of qualia (This is green. This is crispy. This is round. This is tasty. => "This is an apple".) This viewpoint, however, does not correspond well to human understanding of say, a cat, whose existence must be presumed to continue even when it invokes no qualia in humans, whose qualia vary among different cats, and whose death smoothly strips it of its catlike qualia.

In other words, while one can take philosophically consistent worldviews where objects and concepts don't exist, such world views are unfruitful for conducting human affairs: In our lives, we simply need to refer to objects, and pretend that they actually exist as such. One famous story tells of a philosopher, Samuel Johnson, who, frustrated about the philosophical soundness and un-refutability of a fellow philosopher's belief that the physical world does not exist, furiously kicks a rock yelling, "I refute it thus!"

In Lojban, most sumti are made from selbri one way or the other, which means that at the core of most sumti lies a selbri, an action, something which something does. The Sun is not usually referred to as la solri, "The Sun", but often lo solri, "something which is being a sun". There are many confusing philosophical implications of this: As stated before, it's hazy at best what it means "to cat" and when something begins catting or "stops catting". A fictional language with similar properties is described in a neat short story, "Tlön, Uqbar, Orbis Tertius" (where "The Moon rose over the ocean" is phrased using similar verb/adverb-derived nouns: "Upward behind the onstreaming it mooned"). In that short story, the language is about to lead to the collapse of society because the worldview which such a language implies is unfit for dealing with the realities of Earth.

The take home point of all this is: Precise definitions of the different types of sumti are impossible, because these categories do not correspond to the real world. Nonetheless, we need these categories when speaking.

There may possibly be an infinite amount of types, but I'll go through the ones which are dealt with most often in Lojban:

Material objects are perhaps the easiest to understand, even though they're hard to defend philosophically. They always have a place in both time and space, but they're considered to be a constant existing through time. That is, objects are not considered temporally: A banana carries with it its unchanging banana-ness even as it ages, until it begins breaking down and stop being a banana at all. If one could freeze time for all bananas, they would stay bananas during that frozen time.

Events are, like objects, places in space and time, but events are considered as unfolding over time: The temporal aspect is as important as the spacial. A banana can be considered an event, but in that case, the event of being a banana is composed of the changes the banana undergoes over time, whereas what makes a banana an object is all that which doesn't change. Freezing time would also freeze the event of being a banana.

Functions are a term used by a few Lojbanists to describe a group of types. All functions are abstract concepts and as such don't really exist in the real world on their own. The nuts and bolt of functions is the subject of lesson thirty; here, we focus on their semantics alone. There are a few types of functions:

Selbri are something you're already well familiar with. It describes an act of doing or being. crino understood as a selbri means "being green", darxi means "to hit". A selbri on its own is devoid of the sumti who's doing or being that selbri. As such, they're divorced from any particular instance of being green or hitting, and can therefore be understood as a kind of generalized events. They're used for sentences where no particular instance of that selbri being applied comes to mind. For instance, if I'm looking forward to my wedding next Wednesday, I'm thinking about some event placed in space and time (even if the wedding never actually takes place for some sad reason), whereas if I'm saying that I'd like to become married one day, I desire the act of marriage, and thus I desire the selbri, or rather, that the selbri be applied to me.

Amounts have almost the same grammatical properties as selbri, as you'll see in two lessons. Semantically, however, they're quite distinct. An amount is how much something fits a selbri, which is something completely different from the selbri itself. An amount is some kind of number, or can be represented by some number, exact or inexact, no matter whether what is quantified is practically measurable.

There is some disagreement about whether it's correct to use an amount abstraction to quantify something which is in principle unmeasurable. Thus, the amount of my greenness is certainly valid, since that could be measured by say, a digital camera, but speaking about the amount of me being Bob's friend may not be accepted philosophically. A great example which demonstrates the difference between amounts and selbri when applied to specific sumti is the following: "I change in blackness": When "blackness" is considered a selbri, it means that change from being black to not being black or the other way around. When "blackness" is considered an amount, it means my skin turns more or less black (as it does during the winter when there's little sunlight).

Concepts are maybe functions and maybe they're not, depending on who you ask. Their position as maybe-functions is explained in lesson thirty. Concepts, unlike selbri and amounts, cannot be applied to sumti. There can be no talk of fitting a concept, like there can be of whether or not you are fitting a selbri or measuring the amount of fitting a selbri. A concept does not exist in the real world. A concept is not even represented in the real world, like amounts or selbri can be when they’re applied to sumti. A concept, say warfare, exists only in the minds of people, and is understood as the meaning of the word war. Thus "love" understood as a concept is the idea of what love is, no matter who loves and who is being loved.

Perhaps an example can demonstrate the difference between amounts, selbri and concepts:

In "I like loving" and "I like being loved", we are speaking of a selbri.

In the sentence "I like how much I love", I like an amount, and when saying "I like love", I refer to the concept of love.

Bridi is a type which you're also familiar with. A bridi is certainly not a function, but it does bear some relation to functions, as we'll see later. Bridi themselves are imaginary; they exist not in the real world, but inside texts, the next type to explain. However, bridi are not composed of whichever specific symbols are used to express them - because bridi are imaginary, different sentences may express the same bridi. It can be that the sentences are in different languages, that the word order is changed, or that different words are used to refer to the same sumti. Thus mi do prami/mi prami do, "I love you", mi ko prami and do mi prami (when spoken by the person to which do refers in the first sentence) all refer to the same bridi. Bridi always have their full place structure filled by something with a non-zero value.

The concept of a text is close intertwined with the concept of a bridi. All bridi are contained in texts, though not all texts contain bridi. Indeed, one might define a text as something that can contain a bridi, but this can easily lead to circular definitions when attempting to define what bridi are. The current understanding of what things should be considered texts is vague at best. Like bridi, texts are something ethereal, something we can imagine exist in a realm outside the physical world. While these lessons certainly are a text, the text is not made of the paper these lessons are printed on, nor the magnetic fields which constitutes the bytes it's stored on. Those physical media only represent the text. But what exactly can represent a text? Words, certainly. But what about body language? And do actions really speak texts louder than words? This is not an issue I'll attempt to answer or even give a shot in these lessons.

Sets are much easier to deal with. They're a kind of meta-type: A imaginary box, in which a group of sumti is packed into. This box has very little to do with what's inside it. A big set does not mean that the things in the set are big, but that there are many things in the set. Sets have very few properties, therefore sets are only used when speaking about the number of things in a given category, the number of things shared between several categories, the criteria for including things in the category etc.

The last used type is the truth value. I've only seen it in use a handful of times, and only include it here because it'll be relevant when discussing a certain abstraction in the next lesson. A truth value is some verdict that a bridi is true, false, or anywhere in between. The nature of a truth value is a verdict, "True", "False", "Mostly true" or the like. It's often represented by a number, such as 0 (false), 1 (true) or 0.5 (halfway true), but this a simply a representation of the truth value, and not the value itself. One might as well represent it by a color, ranging from red to blue.

Lesson 29: Semantics of simple abstractions

Having acquired a terminology suitable for the discussion of types, we can now more easily take on the semantics of abstractions. Most often, an abstraction is merely a bridi considered as a certain type. We begin with what I consider the simplest of abstractions:

nu = x1 is an event of BRIDI happening

You're already familiar with this word and how it's used. A nu-abstraction is always an event, and as such, it's situated in one particular time and space. Thus:

mi catlu lo nu lo prenu cu darxi lo gerku
I watch a person hitting a dog

is a proper event, whereas

mi kakne lo nu bajra fi lo mi birka
I can running on my arms.

is wrong, because no particular event of running is implied: The running you're able to do is a selbri - a generalized event, and the Lojban sentence above should sound as badly phrased as its English translation.

There are many ways to view an event, and so there are four other abstractors, which all also create events. The meaning of these abstractions are all covered by nu, but more specific. I'll go through them all here:

mu'e = x1 is a point-like event of BRIDI happening
za'i = x1 is a state of BRIDI being true
pu'u = x1 is a process of BRIDI unfolding through stages x2
zu'o = x1 is an activity of BRIDI consisting of the repeated event of x2

The understanding of these abstractors is tied to the understanding of event contours. mu'e is akin to the event contour co'i in the sense that both treat the bridi as point-like in time and space:

lo mu'e mi kanro binxo cu se djica mi
Me becoming healthy is desired by me

has the semantic meaning that the process of becoming healthy is not being considered. If it consists of painful chemotherapy, it is plausible that this process is not desired at all. Becoming healthy, in a point-like sense is desired, however.

za'i is like the event contour ca'o in the sense that lo za'i BRIDI begins to apply when the bridi begins and sharply ends when the bridi ceases to be true, much like ca'o.

za'o za'i mi kanro binxo means that the state of me becoming healthy took too much time; that the time between my health beginning to improve and be actually being healthy was long-winded.

The actual treatment is perhaps better caught by pu'u, which, like event contours in general, puts emphasis on the entire event as unfolding through time. .ii ba zi co'a pu'u mi kanro binxo .oi expresses fear that the painful process of becoming healthy is about to begin. The x2 is filled by a sequence of stages, which can be made by interspacing the stages with the non-logical connective ce'o: ze'u pu'u mi kanro binxo kei lo nu mi facki ce'o lo nu mi jai tolsti ce'o lo nu mi renvi means something is a long process of me becoming healthy consisting of the stages A ) I find out B ) something about me begins C ) I endure.

Finally, the semantics of zu'o treats the abstraction as consisting of a number of repeated actions:

lo za'a zo'u darxi lo tanxe cu rinka lo ca mu'e porpi
The observed activity of beating the box caused its current brokenness.

is more accurate than the similar sentence using nu, because zu'o makes it explicit that it was the repeating of the action of beating, not a particular instance of beating which broke the box.

The x2 of zu'o is either one event or a sequence which is repeated. To be unnecessarily explicit, we could have stated that the cause of the current brokenness was lo zo'u darxi lo tanxe kei lonu lafti lo grana kei ku ce'o lonu muvgau lo grana lo tanxe kei ku ce'o ... and so on.

Note the difference between mu'e bajra, za'i bajra, pu'u bajra, zu'o bajra and nu bajra: The point-like event of running puts emphasis on the event happening, but nothing else. The state of running begins when the runner begins and stops when the runner stops. The process of running consists of a warm-up, keeping a steady speed, and the final sprint. The activity of running consists the cycles of lifting one foot, moving it forward, dropping it down, repeat with the other foot. All of these aspects are simultaneously covered by the event of running, nu bajra.

Another type of abstractor is the experience abstractor, li'i:

li'i = Experience abstractor: x1 is x2's internal experience of BRIDI

An experience can be considered an event type. It has almost the same attributes: It's placed in space, there's focus on the time over which it unfolds, and it's not a function.

Unlike event abstractions, however, an experience is explicitly mental - a li'i-abstraction cannot be said to exist outside the mind of a person. This difference is purely semantic, and exchanging event and experience abstractors would not be considered a type failure in the same sense as mi kakne lo nu.... It might not make sense, as in lo kacma cu vreji lo li'i lo mi pendo cu cliva kei mi - A camera recorded my experience of my friend leaving. But then again, cinema is dependent on cameras being able to record the actors' emotions.

It does, I think, make complete sense to write mi ciksi lo li'i lo mi pendo cu cliva kei mi, lo li'i lo mi tunba cu morsi cu mukti lo nu mi catra, and the like.

li'i is derived from lifri, and is indeed a se lifri - an experience.

A du'u-abstraction is probably the other kind of abstraction you're used to seeing, beside nu.

du'u = Bridi abstractor: x1 is the bridi of BRIDI, as represented by text x2

According to the standard, abstractions like truths, lies, things being discovered or things being believed are all pure bridi:

.ui sai zi facki lo du'u zi citka lo cidjrpitsa
Yes! I just found out that pizza will be eaten soon!
mi krici lo du'u la turni cu zbasu pi ro lo munje zi'o
I believe The Lord created all of the universe.

What is being discovered or believed is the truth of an abstract bridi, so du'u is appropriate.

As you can see from the definition of ‘'du'u, the x2 of du'u is used for the text in which the bridi is contained. As stated before, the nature of texts is hard to nail down, but in practice, du'u's x2 can be used to express indirect quotation:

.ue do pu cusku ku'i lo se du'u do nelci lo ckafi
Oh! But you said that you liked coffee!

Out of obligation, this lesson will include the truth value abstractor, jei. Let's see the definition:

jei = Truth abstraction: x1 is the truth value of BRIDI under epistemology x2

jei is rarely used, not because truth abstractions are infrequently needed, but because most Lojbanists use other mechanisms to obtain them. The real use of jei is whenever a truth value which is not "true" or "false" is needed, i.e. practically never. I'll give a couple of examples:

mi di'i pensi lo jei mi merko
I often think about whether I am American or not.

(contrast with I often think about how American I am, which uses an amount abstraction, not a truth value)

li pi bi jei la tinjin cu mikce
It's 80% true that Tindjin is a doctor.

(whatever that might mean)

To conclude this lesson, the abstractor su'u is a universal abstractor, whose x2 can be used to specify how the abstraction should be considered - for example, which type the abstraction is. It has already been defined, but we might as well do it again:

su'u = Universal abstractor x1 is the abstraction on BRIDI considered as x2 / x1 is the abstraction of BRIDI of type x2.

The idea of this abstraction is easy, so I'll just give a few examples of it in use and leave it at that:

The English phrase that I love you is definitely a sumti, since it's meant to function as a subject or object in a sentence. It's also clearly made from an abstraction. It can therefore be translated lo su'u mi do prami. Without the context of the English sentence, though, it's hard to guess what kind of abstraction was meant. I will die happy by the time that I love you. treats the abstraction as an event happening in time. The truth is that I love you. treats the abstraction like a bridi, which can be considered true or false. "You don't know how much I love you" treats the (nearly identical) abstraction as an amount. Using the second sumti place of su'u, these can be explicitly differentiated:

lo su'u mi do prami kei be lo fasnu is an event.

lo su'u mi do prami kei be lo bridi is a bridi.

lo su'u mi do prami kei be lo klani is an amount.

Using su'u this way, the semantic (though not grammatical) range of all abstractors can be covered. More usually, though, other abstractors are used.

Finally, Lojbanist J. Cowan translated the title of the book The Crucifixion of Jesus Considered As A Downhill Bicycle Race as lo su'u la .iecuas. kuctai selcatra kei be lo sa'ordzifa'a ke nalmatma'e sutyterjvi.

Lesson 30: Semantics of functions

Functions are a group of two-three types of abstractions. The term's not official, but I'll use it here anyway.

The definition of functions is closely related to the neat little word ce'u. ce'u is a sumka'i which fills one sumti place. It's only found usage inside abstractions which are also functions. All functions can have at least one ce'u somewhere in the abstraction - that's what makes them functions. The ce'u can be elided, in which case it's most often assumed to fill the first elided sumti place of the function, unless context provides a more reasonable alternative.

What does it actually do? Let's have a look at its definition:

ce'u = Pseudo-quantifier binding a variable within an abstraction that represents an open place.

Well, that wasn't very helpful, so let me try explaining it with another approach:

Putting ce'u in a sumti place leaves the sumti place empty. The place is not erased, like if you fill it with zi'o, but the place is not filled with anything - not a specific thing, not a zu'i, not a zo'e, nothing. In that manner, the empty sumti places are reminiscent of the x1, x2, and x3's we put in the sumti places of English definitions of brivla - marking "This is where something else can be put".

Thus mi citka lo ti badna is "I eat this banana", but mi citka ce'u is "I eat X".

Of course, "I eat X" is meaningless unless that X is filled by something, and indeed the sentence mi citka ce'u is senseless in Lojban as well.

In order to put it to use, we need a function abstraction. We'll begin with the most often-used: The selbri abstraction ka. Let's see its official gloss:

ka = Property/quality abstractor (-ness); x1 is quality/property exhibited by BRIDI.

Under the understanding which I will teach, this gloss is mildly misleading. Instead, ka should probably be glossed such:

ka = Predicate/selbri abstractor: x1 is the predicate/selbri of BRIDI (needs at least one open variable i.e. a "ce'u")

Using a selbri abstraction, "I eat X" can make sense, as in the following example:

ckaji = x1 is characterized by selbri x2

lo ti badna cu ckaji lo ka mi citka ce'u - "This banana is characterized by the selbri: "I eat X"", which may be rephrased as "This banana fits the selbri: "Being eaten by me"", which is of course equivalent to mi citka lo ti badna - "I eat this banana".

For the statement to make sense, the sumti place held open by ce'u usually, but not always, must be filled by something. The main selbri of the statement, in this case ckaji, gives us a clue how to fill the open sumti place. Such selbri almost always fill it with a sumti from the main selbri. How ce'u is given a non-zero value has been a subject of minor debate in Lojbanistan, but the issue is more or less settled: ce'u keeps a sumti place open, and the main selbri then fills it with something, and what fills the place depends on the selbri in question.

Though it often is, the ce'u place need not always be filled by the selbri in order for the abstraction to make sense: On its own, lo ka ce'u te vecnu lo finpe means: "buying a fish", or "to buy a fish". This can be used in a sentence without the selbri filling the ‘’ce’u’’ in:

lo se lisri cu srana lo ka ce'u te vecnu lo finpe - "The plot is about buying a fish". Here, srana does not apply anything to the ce'u-place, and the abstraction is instead seen as the selbri on its own.

An alternative way of explaining ce'u is by regarding the word as representing variables in a lambda function. For instance, consider the sentence:

la .alis. cu djica lo ka ce'u te vecnu lo finpe - "Alice wants to buy a fish"

Here, the first argument of djica is the one who wants something, namely Alice. The second argument is the selbri that Alice wants to fulfill: Buying a fish.

We can view ce'u as a free variable, which then becomes bound by a lambda abstraction, namely ka. Now, ka ce'u terve'u lo finpe can be seen as a lambda function:

\ x -> te vecnu(x,lo finpe,zo'e,zo'e),

and in this case djica supplies the lambda function with Alice.

Lambdas can be stored, allowing them to be passed around and use them in various situations:

ca'e ko'a ka ce'u dansu .i mi ko'a ckaji .i do ko'a djica .i ma'a ko'a kakne - It is dancing. I am doing it. You want it. Everyone can do it."

Now, using ka, you can correctly phrase "I can run on my arms". How?

Answer: mi kakne lo ka {ce'u} bajra fi lo mi birka

A lot of often-used gismu take selbri as one of their sumti, which means lo ka is used quite often. A few notable examples are troci, kakne, djica, zukte, snada and fraxu:

lo xasli na’e kakne lo ka silcu la'e la'oi X-files - "The donkey cannot whistle the X-files song"

.e'o ko lo jai se zgike cu fraxu lo ka darxi lo damri ca lo nu do sipna - "Please forgive the musician for striking the drum when you were sleeping!"

At least one selbri can fill two ce'u within a ka-abstraction, namely ‘’simxu’’. What does the following jufra mean?

mi lo pampe'o cu simxu lo ka {ce'u ce'u} gletu

Answer: Me and my lover have sex with each other mutually"

Of course, the ce'u need not be placed in the beginning of the ka-abstraction, though it is by default. One could very well speak of:

lo ka la .bab. melbi ce'u - "The selbri of: "Bob is beautiful according to X"", or in other words: "Thinking that Bob is beautiful".

Indeed, moving the ce'u around in an function creates very different meanings:

lo ka ce'u panzi la .maik. - "The selbri: "X is a child of Mike"" = "Being Mike's child", versus

lo ka la .maik. panzi ce'u - "The selbri: "Mike is a child of X"" = "Being the parent of Mike".

One could even imagine a statement in where the ce'u is placed in a very unconventional place, that nonetheless is quite intuitive:

mi .e nai do ckaji lo ka lo bruna cu jbocre, wherein the ce'u is elided, but most probably hiding in lo bruna be ce'u, therefore meaning "I and not you is characterized by the selbri: "The brother of X is good at Lojban"", which is the same as "I have a brother who's good at Lojban, but you don't".

One can make a function, like a "ka"-abstraction, and fill all sumti places, leaving no place for a ce'u. The resulting bridi are weird:

mi kakne lo ka mi merko lo mi bangu - "I can my language is American". This is clearly a type error. Some people regard functions without any ce'u to be equivalent to bridi abstractions, so that:

mi krici lo ka mi vrude la cevni is the same as mi krici lo du'u mi vrude la cevni - "I believe that I am good in the eyes of God", and is just as good a sentence in Lojban as its translation is in English. In my opinion, one should refrain from using any of the function abstractors if one doesn't want to use a function. If you mean du'u, use du'u.

The other abstractor which clearly can provide a function is ni. Like ka, a ce'u can be placed in a ni abstraction, but unlike with ‘’ka’’, using a ‘’ce’u’’ with ‘’ni’’ is not mandatory. Thus, if no ce'u is placed in a ni-abstraction, one cannot assume that it's elided - it might simply not be there. If the main selbri is not one which clearly tells us how to fill a ce'u-place, such as zmadu or mleca, there's probably no ce'u at all.

In all other aspects, the way ce'u works within the abstraction is just like ka, so the difference is purely semantical. Whereas ka creates a selbri, ni creates an amount. Here's the definition of the word:

ni = Amount abstraction: x1 is the amount of BRIDI on scale x2

Being familiar with ka, the usage of ni should be straightforward:

mi zmadu do lo ni {ce'u} xekri - "I exceed you in amount: "X is black"", or: "I'm blacker than you." As stated in lesson twenty-eight, all agree that this makes total sense because the brightness of one's skin could be measured by a camera. However, some people will not accept the unmeasurable:

mi zmadu do lo ni mi pendo la .maik. - "I am more of a friend of Mike than you are". I think using amounts to quantify the unmeasurable is fine, but that is an issue I swept under the carpet two lessons ago, and I'm not gonna take it on here.

It's absolutely clear, however, that it's wrong to use ni as a way to enumerate how many objects fit a selbri - it's always about to which extent certain sumti fit a selbri. Thus:

do mleca mi lo ni panzi ce'u means "You are less of a parent than I am", and not "You have fewer children than me".

In case you're curious (I was), the jufra zo'e panzi ce'u in the previous example actually refers to two distinct bridi, because the selbri fills the open ce'u-place twice, once for do, and once for mi, making the two sub-bridi: zo'e panzi do and zo'e panzi mi. Since these two bridi are considered different, the zo'e need not refer to the same object.

What does it mean if you don't use a ce'u inside a ni-abstraction? Well, then the main selbri can't fill any of the sumti in the abstraction, so when using selbri like zmadu and mleca, there's a good chance it won't make any sense. However, if ni itself is the main selbri, it's totally fine to avoid using any ce'u at all:

li du'e ni do nelci lo vanju
You like wine too much.

The last of the abstractors we treat in this lesson is si'o, the concept abstractor. si'o may be considered a function, or it may not be considered a function. A si'o-abstraction certainly contains a ce'u - in fact, under the understanding which I am teaching, a si'o-abstraction always contains nothing but ce'us! These ce'us, unlike those of ka or ni, remain open and cannot be filled by any selbri. In other words, the function cannot be applied to anything, which is what makes it a maybe-function.

si'o = Concept abstractor: x1 is x2's concept of BRIDI

Let's have a few examples:

lo si'o xebni, which, because all the sumti places are filled with ce'u is equivalent to:

lo si'o ce'u xebni ce'u - "The concept of: "X hates Y"" = "The concept of hate" = Hate

The mythical creatures Balrog from Lord of the Rings are described as being "shadow and flame", the poesy of which appears much stronger in Lojban: la balrog cu si'o fagri joi manku is asserting not only that it’s made out of shadow and flame, but also suggesting that it’s the prototypical Shadow and Flame, from which all other shadow and flame derives.

For good measure, it should be stated that etymologically, "si'o" derives from "sidbo", "idea", but in current usage an idea is considered a text and not a concept.

The difference between the three abstractors ka, ni and si'o can be illustrated with a few more examples for comparison:

lo ka crino cu pluka mi
Being green pleases me
lo ni crino cu pluka mi
How much {zo'e} is green pleases me (no ce'u!)
lo si'o crino cu pluka mi
Greenness pleases me
mi nitcu lo ka sipna ku lo ka kanro
I need sleep in order to be healthy
mi nitcu lo si'o sipna lo ka tavla fi lo sipna
I need the concept of sleep in order to speak about sleeping things

And I was tempted to write mi nitcu lo ni sipna ku lo ka vreji ri - "I need the amount of how much {zo'e} sleeps", but that doesn't seem to make a lot of sense.

Lesson 31: The not-so-cute assorted words

Yes, this lesson is yet another which focuses on assorted words. This time, however, the content of the lesson is not chosen by common usage: Unlike words like jai and si, most of the following words see little usage in ordinary conversation. Some of them are, however, important to understanding the following lessons, and so these words must be awkwardly placed before their usage in these lessons.

Before we venture to obscure words, there's one word which I think deserves a more thorough explanation than it has been given so far: kau.

kau was explained in lesson twelve, but the real implications of it was not. If you have forgotten what it means, I advice you to go back and see. Unfortunately, I can't present a theory on what kau does when it's present in the main bridi, only on what it does inside an abstraction.

A bridi with abstraction containing a kau makes two claims: The bridi itself makes one claim as usual, and implicit in the abstraction is furthermore the claim that the word kau is attached to has a real, nonzero meaning.

This should be demonstrated: The bridi mi pu viska lo nu ma kau cliva le salci (I saw who left the party) makes two claims. First, it makes an implicit claim that the ma refers to something real. That is, the bridi actually claims that da cliva le salci (X left the party). Secondly, the main bridi makes the claim that what the ma refers to is what was being seen, or in lojban mi pu viska lo nu da cliva le salci. (I saw that X left the party)

This principle is not restricted to the abstractor nu, or to the question word ma. The same principle can be extended to any other abstractor and any other question word, as in the following bridi:

la .bab. na'e birti lo du'u xu kau la .mias. pampe'o (Bob isn't sure whether or not Mia has a boyfriend) states firstly that xu applies, which means that a truth value correctly can be assigned to the bridi, and secondly that what Bob isn't sure about is the correct truth value for the bridi.

kau can also be applied to a non-question word. This doesn't really change the meaning of the word. The same procedure still applies:

do ca'o djuno lo du'u la krestcen kau cu cinba la an
You already know that it was Kristian, who kissed Anne.

states firstly that la krestcen cu cinba la an and then that do ca'o djuno lodu'u la krestcen cu cinba la an.

Moving on to the more obscure words, we can begin with xi; it's easy.

xi = Subscript. Converts any following number string to a subscript, which has the grammar of an attitudinal (ie. placable practically anywhere).

There are few officially encouraged uses of xi, but precisely because the construct xi+number has the free grammar of an attitudinal, the possible uses of xi are almost endless. In general, it's used to enumerate any word, variable or grammatical construct, as opposed to what it refers to. Let's see some examples.

la tsani cu cusku zo coi .i ba bo la .triliyn. cu cusku lu .ui coi la tsani coi la klaku li'u .i ba bo la klaku cu spusku fi lu coi ty. xi pa .e ty. xi re do'u zo'o li'u
Tsani said "hi", then Triliyn said "Hey Tsani, hey Klaku :)", then Klaku answered "Hello T1 and T2 :P".
spusku = x1 makes a reply x2 (text) to x3

Because it's the standard that ty. refers to the last sumti which began with T, ty by itself as said by Klaku would have referred to Tsani. Two different ty. can be made by subscripting with xi.

If the rare situation arises that we need more variables of the type da or bu'a that there are in the language, an infinite number can be made by simply subscripting any existing with a number. Note that a non-subscripted variable is not defined of being equivalent to any subscripted one. That is: ty is not always equal to ty xi pa or ty xi no or anything of the sort. I expect this to be rarely used, because any sentence with more than 3 da-like words or more than 10 ko'a-like words would be hard to keep track of.

Second, we have ki, of which I am not aware of a single usage in my time on IRC; probably not because the word's useless, but because few Lojbanic texts are of the kind where you need it.

ki = "Sticky tense". Set/use tense default; establishes new open scope space/time/modal reference base.

Any row of tense words can be suffixed with ki to make the tense(s) apply to all following bridi. When, for instance, telling a story, this can be used to make explicit that the default time - the time as meant without any tense words - is the time the story is placed in. Usually, this will not be necessary; beginning a fairytale with pu zu vu ku, one can assume that the entire tale is happening a long time ago and far away. Let's have an example:

pu zu vu ki ku zasti fa lo pukclite je cmalu nixli goi ko'a .i ro da poi pu zu vu viska ko'a cu nelci ko'a
Once upon a time there was a sweet, little girl. Everyone who saw her liked her.

The ki allows us to elide the three tenses in the second bridi, and in all the bridi to follow.

So, if a bunch of tenses have been make sticky with ki, how do we unstick them? Simply use ki by itself, and all sticky tenses are made unsticky.

Lastly, several sets of tenses can be made sticky by subscripting ki. If there are several of such sets in usage at any given time, one can use the subscripted kis to make the corresponding set of tenses apply. Unsubscripted ki alone still makes all tense stickiness disappear, so you have to be careful not to use ki unsubscripted if you plan on using several sets of tenses.

Changing subject. There's a set of sumtcita which are often used, but which I dare not try to define if not under the disclaimer of part three. Let's see official definitions for two of them first.

ca'a = modal aspect: actuality/ongoing event. Bridi has/is/will happen during under the circumstances of {sumti}
ka'e = modal aspect: innate capability; possibly unrealized. Bridi is possible under the circumstances of {sumti}

Let's first contrast ca'a with ka'e. ka'e means that the bridi is "possible if the event of SUMTI has/is/will occur". ca'a by contrast, means that the bridi "has, is, or will happen if the event of SUMTI has/is/will occur".

Like all sumtcita, their corresponding sumti can be elided if the sumtcita is placed before the selbri:

le vi sovda ka'e fulta .i ja'o bo ri fusra - "This egg floats. Therefore, it's rotten".

By using ka'e, this sentence does not state that the egg has floated, or ever will float, but rather that it could float.

pu'i = modal aspect: can and has; demonstrated potential. Bridi could or could not happen, but in fact it is/did/will happen under the circumstance of {sumti}
nu'o = modal aspect: can but has not; unrealized potential. Bridi is possible, but is/will/have not happened under {sumti}

Understanding ka'e and ca'a, nu'o simply means ka'e je na ku ca'a, and pu'i means ca'a je ka'e na ku.

Historically, these four words was tense sumtcita - therefore the "modal aspect" in their definitions. All tense sumtcita was then not considered sumtcita at all, but rather "selbri tcita". A modern understanding of Lojban is gaining popularity, wherein the tense sumtcita are considered sumtcita, almost exactly like the BAI, and in where selbri tcita are not used.

Because of these four words' history as selbri tcita, they can be freely elided - indeed, since one of the four words always applies, one is always assumed to be elided. This is most often ca'a. Indeed, it's so often ca'a that one could wonder why ca'a is not the default.

One reason is that some selbri has two useful definitions, one which implies ka'e SELBRI and one which implies ca'a SELBRI. For an example, see fasnu, which can mean "x1 is happening" or "x1 is an event", where the first implies ca'a fasnu and the second ka'e fasnu

Another use of "implied ka'e" is as a way to escape an annoying philosophical problem in the language. A selbri only applies if all its places apply too. For some selbri, like kabri, that's a problem.

kabri = x1 is a cup containing contents x2 and of material x3

The definition suggests that if the content of the cup is removed, the x2 no longer applies and it stops being lo kabri. Implied ka'e, or more fittingly, nu'o, let us escape that problem.

End of lessons

Sorry, but as of now, there are no more lessons in this series. Perhaps more will be added later.