Lojban Wave Lessons/25

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Lojban Wave Lessons: Foreword | ← Lesson 24 | Lesson 25 | Lesson 26 →

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

Lojban Wave Lessons: Foreword | ← Lesson 24 | Lesson 25 | Lesson 26 →