Lojban Wave Lessons/26

From Lojban
Jump to navigation Jump to search
Lojban Wave Lessons: Foreword | ← Lesson 25 | Lesson 26 | Lesson 27 →

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.

Lojban Wave Lessons: Foreword | ← Lesson 25 | Lesson 26 | Lesson 27 →