LoCCan

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by la pycyn:

Lojban profited richly from problem that were found in Loglan and left unsolved there. But Lojban has also given rise to some problems or useful suggestions that cannot be dealt with within Lojban itself. LoCCan is the concept name for the third generation of logical languages, to build on Lojban as it did on Loglan. Needless to say, such a language will not come into being in reality, but like concept cars it will serve as a reservoir of ideas that may someday find places in Lojban.

Note 1. Prepositional Connectives

There has been from time to time a discussion of a structure consisting of a set of sentences - more than two - which could then be modified in various ways to get the harder multi-sentence connections without repetition: "all or none," "exactly two" and so on. Notice that some odd ones are easy to get: "an even number" is just iterated ico in an even-numbered set, the same with one negation in it for an odd-numbered set. The reverse holds for "an odd number." This is a possible consideration for LoCCan, though its usefulness is probably severely limited. On the other hand, having the possibility available might increase the number of uses. Still, most of the things one seems to need to say can be worked out sequentially.

Perhaps more useful is a rethinking of the connective system altogether. One might, for example, use the Lukasiewicz notation system, which identifies the connective by indicating the lines on which it is true. If we modify this to also allow indicating the lines on which it is false, then we would never need to mention more than two lines. Using T to stand for whatever we would ultimately use to indicate that we are showing true lines and F for the corresponding false cases, we could then refer to the lines by the vowels now used for connectives. AND would then be Ta, OR Fu, IFF aTu (or eFo) and XOR aFu (or eTo). De Morgan is very simple: just interchange T and F. This system could be easily extended to connectives of more than two places: using V'V gives expression to 16 lines, enough for 4-placed connectives. Alternatively, Vi would give eight lines, enough for three places. Combining these is more of a problem, however, since the three-place connective may require four lines in the definition. This is probably not significantly shorter - and probably much harder to interpret or create - than doing the same with two-placed connectives, repetitions and all.

Another approach is simply to read off the resultant column from top to bottom in binary and use the resulting number, in decimal or, more naturally, hexadecimal. Moving to a higher number of places take minimal addition. Negation of n in any given number of places is just subtracting n from the maximum from that number of places. So, in 2-place, AND is 8. NAND is therefore 7, 15 (or F)- 8. OR is 14 (E), one less than the highest, so NOR is 1. IFF is 9 so XOR is 6. And so on. Note that the generalizations of OR and AND occupy the same relative positions as however large the number of places: OR is just below the maximum, AND is the last item in the top half. Constructing connectives on the fly is relatively simple, since the number for the connective that is true on lines a,b, ..., n is just the sum of the numbers for connectives true on only a and on only b ... Note that, unlike the various other scheme, including the one now in use, TAUT and CON do not need special treatment: the latter is 0 always, the former FF... as far as is needed. But, even for Taut, the notation needs to note how many places are involved, since the same numbers turn up in all cases, but with very different meanings (8 in a three placed connective is ~P & Q & R, not AND).

Note 2: The Connective System

The current connective system works pretty efficiently except that it eats up cmavo space: twenty-one words for four concepts. The following has no other obvious virtues that freeing up this space.

So, suppose we used only eks and whatever had to be added to cover hard cases. Generally speaking, forethought connectives present no problems, since what comes between the connective and gi determines what comes after. So what follows is - except as noted - about afterthoughts. In general, we can mark forethought connectives of any sort by a separate word, say gu, thus saving three forms (I don't think that using gi as in the current usage for nonlogical connectives is trouble-free, but that issue needs looking at - to save yet one more bit of CV space.)

After a connective in a significant way can come the beginning of a sumti, a brivla, a preposition (tense/aspect/modal) or an abstractor (I am skipping MEX, though I don't think it will offer any special problems once we understand the basics).

We can first separate off the cases where what comes along begins a sentence. It is important to note that it is a new sentence, not a compounding within another sentence, whatever the beginning may be. But new sentences already have a mark, i. So, placing this directly after a connective clearly shows the status correctly: la djan cu klama e.i la meris cu stali

Not at the beginning of a sentence, a sumti will follow a connective only as a parallel to another sumti. This is already the purest use of logical connectors and needs no modification when only eks are used.

A following brivla, however, opens a range of cases, poorly dealt with in CLL (either not at all or confusingly). A following brivla may be 1) part of a compound predicate in a description, if what precedes the connective is a description ending in a brivla; or 2) the beginning of a later part of parallel bridi tails, regardless of what precedes; or 3) a later part of a tanru-internal connection.

The case of compounds within descriptions is not dealt with in any one place or in any thorough way in CLL. It cannot be subsumed under any of the ordinary cases, because, unlike them, it requires that some of the elided places - the first, in fact - be the same in all the variants (a problem we will have to take up again in dealing with quantifiers). So, lo citno a prije cu klama does not come from lo citno cu klama a.i lo prije cu klama. On the other hand, as we will see, they do not come from tanru internal connections either. For present purposes, however, it turns out to be best to take these connections as basic: when this might apply, the unmarked form is of this sort. When the preceding part ends in a brivla of a description and the following part begins with a brivla, we need an explicit ku at the end of the description if the following brivla is not to be a part of it.

When the preceding part does not end in a brivla of a description (whether because it ends in ku or something else), we have another ambiguity possible: is ti broda e brode brodi the compound of two bridi tails or a tanru-internal compound modifier. The two versions have different groupings: ti (broda) e (brode brodi) vs. ti (broda e brode) brodi, different possible further combinations, and, of course, different sources: ti broda e.i ti brode brodi vs. ti broda brodi e.i ti brode brodi. So we need some way to distinguish them. This is equally true for the forethought cases. But it would seem that a single marker, ji say, before the connective (or the gi in forethought mode) would be sufficient. Notice that even this is not needed if the broda part has arguments, as the difference between bed and unbed forms suffice. (CLL is confusing on tanru-internal connections, trying to distinguish them from bridi tails when there is not third brivla involved and at one point even seeming to identify broda brode with broda e brode and then denying that the distribution goes through as a ground for the distinction).

Finally, a connective can be followed by a preposition (the case of abstractors does not appear to present any problems). Tense/aspects cases may be simply compound tenses, but even those can be complex: is the whole string of tenses before the connective to be joined to the whole string after or just the last one and the first one after? To some extent this can be handled by the fixed order of tenses, but these are not absolute, so some further device may be needed.

Supposing that that situation is not involved, we have the possibility that what is presented is 1) connected sumti tcita, 2) connected prepositional phrases, or 3) tensed connectives. The first presumably reduces to the case of connected tenses, even when the items connected are not both tenses. Connected prepositional phrases seem to be the norm when such are possible: pa ti e ba, say, and so can go unmarked. But the same context can be a tensed connective, with the ba followed by bo, not ta, say. The bo cannot be moved to the front, so something else needs to be inserted to attach the ba to the connective. It is unclear whether what was used to distinguish tanru-internal connection would also work here, but, if it does, it breaks up several patterns to do so, requiring a new rationale.

I am not sure that there are not other problems at connectives nor that all or any of these suggestions would even give rise to coherent grammars. But they do free up at least 13 cmavo.

Discussion


  • xorxes:
    • This reminds me of a proposal I once made. I took jeks instead of eks as the basic form, because jeks are already used for most logical connections, but of course any form will do. First we extend the grammar of JA to that of JOI. That takes care of eks, which simply become jeks, except that you need to use an explicit ku a few more times: le broda ku je le brode instead of le broda .e le brode. geks are also already covered, just as we have joigi... gi... for forethought joi, we would have jegi... gi... instead of ge... gi.... giheks would be replaced by gejeks, i.e. geje instead of gi'e. guheks I would simply abolish, but if they are really wanted they can be replaced by gujeks, i.e. guje instead of gu'e. This means we would be using only eight words: ja, je, ji, jo, ju, gi, ge, gu instead of the current twenty-six.
      • You forgot to count the five question connectives: ji, je'i, ge'i, gi'i, gu'i.
        • Thanks. Sorry I missed your system in my casual run through my archives. Using jeks is clearly better than eks for tidy compounds (the glottal stops are a pain), but it is hard to justify new assignments for the V forms. Similarly, the following gi should handle the forerthought problems. I haven't worked out what all the implications of the system are in the hard cases, but it does look like the reduction holds (Yes, I did forget the questions, but they - or it - would just fit right in). The questions about hard cases - and where the kus should go - needs a little statistical information.