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Jorge Llamb�as, On 23/09/2012 21:20:
On Sun, Sep 23, 2012 at 10:58 AM, And Rosta<and.rosta@hidden.email> wrote:2. All connectives are essentially abbreviations of an extensionally-defined set defined by explicit listing of members in combination with quantification over members of the set (e.g. "or" = at least one (is true); "and" = each (is true)),That works for symmetric connectives. For asymmetric ones such as "if-then" we need an ordered pair,
We don't *need* an ordered pair, since the connective is underlyingly symmetric. But by taking advantage of ordering a greater degree of abbreviation is achieved (by doing without an overt negation).
and quantificational predicates don't form a naturally closed class. For termset coordination, what is required is a list of ordered n-tuples, plus quantificational predicates, plus method of expressing an open proposition (i.e. property/relation), plus predicate (ck-, iirc) relating the open proposition to what binds the unbound variables within the open proposition. The special bits of grammar required for this are: * method of listing -- doesn't exist yet * method of listing ordered n-tuples -- doesn't exist yet (we had a method for ordered pairs, but not n-tuples). * method of expressing open proposition -- we have this, but I can't remember now how we did it; at any rate, it's the method for doing "who loves who", either something like "la fa xi smi xu smu prmiku" or maybe "xiku prmiku". E.g. "Some-but-not-all of {<Alice, Alfie, anemones>,<Bertha, Bill, begonias>,<Chloe, Charlie, chrysanthemums>} are in-the-relationship who-gave-who-what"We have a method of listing pairs (g-/jek-) and one of ordered pairs (p-/je'ek-), that can be extended to n-tuples. We don't have the quantifier some-but-not-all, but using "some" instead: sa {jeka<je'eka ma lsi je'eka ma lfi nmna> jeka<je'eka ma brta je'eka bli bgna> <je'eka ma klo je'eka ma tcrli krsntma>} le fe xikoku smikoku dndikuko ckeka
Something like that. There needs to be a distinction between the union of two sets, making {a, b, c, d} out of {a, b} & {c, d}, and a set with two sets as members, making {{a, b}, {c, d}} out of {a, b} & {c, d}. Also, because quantifiers form an open class, the 'pure' version would be:
la {jeka<je'eka ma lsi je'eka ma lfi nmna> jeka<je'eka ma brta je'eka bli bgna> <je'eka ma klo je'eka ma tcrli krsntma>} li smi [quantifier]ika le fe xikoku smikoku dndikuko ckeki
--And.