Subject: Re: [lojban] polyadic connectives

From: [email-masked]
Date: Sat, 18 Aug 2001 18:04:55 EDT

My sermon delivered and the world still standing (another one?), I've tried 
to find the notes from that ancient discussion on this issue, because 1) I 
never want to do those calculations again or reconstruct the program for them 
and 2) there were as I recall some fun cases turned up. But some notes on 
the present discussion.
A) Lojban can express any n-adic logical connective. it just takes a while 
in some cases (at the worst, it involves disjunctive normal forms: 
representing each line of a truth table by a conjunction of the atomic 
sentences or their negations depedning on whether the value on the line is T 
or F [for another discussion: this can be said without indirect questions] 
and then disjoining all the respresentatives of lines on which the compound 
is true. Happily most cases can be simplified (but not all).
B) The problem we were working on earlier was two fold i) what n-adic 
connectives could we express using the n atomic sentences each only once 
(with n-1 two-place connectives) or ii) what did we get from running together 
various combinations of binary connectives. As far as I can remember (others 
seem to ahve this better than I already) we got a strange collection, with 
very few of the things we expected: we could extend "or" and "and" 
indefinitely of course, but not "iff" or "xor" and noting like "if" (although 
we disagreed about what an extension of that would be like). And we got weird 
combinations, like "an even number true" and "all, none or 7 true," but few 
of the more natural "exactly 3 (of 4 or more) true" and the like, whence the 
device for setting up a heap of things and quantifying into (which I can't 
now remember nor how it works with sentences). I think we found nothing that 
worked like conditions, in any useful way (assuming we knew what that was, 
but "if then else" is presumably a paradigm). I suppose that "depending on" 
continues that hunt, with those heaps --or ordered versions of them -- 
playing some useful role (moving up CASE, then).