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Re: [lojban] Re: Using continuations to model quantifiers, focus, and coordination



Joel Shellman wrote:
>> There is a theory of grammar that maps sentences onto logical functions,
>> but this theory has trouble handling quantifiers like "everyone",
>> "someone", and "only".  If I want to parse "Matt spoke", I can treat
>> "Matt" as an individual and treat "spoke" as a function that maps an
>> individual onto a truth value (given X, did X speak?).  But if I use the
>> same system to parse "Everyone spoke", "everyone" is not an individual
>> but a function in itself (given an individual X and an action Y, did X
>> do Y?).  Furthermore, if we turn to the sentence "Matt spoke to
>> everyone", it seems like we need to interpret "everyone" as a function
>> of another type.
> 
> 
> I'm not sure I follow. To me, everyone is the set of all people (or
> possibly less or different depending on context--"everyone in the
> room" is the set of all people present in that room).
> 
> Applying functions on sets shouldn't be a problem, is it?

I suspect that rephrasing all of this in terms of set theory would run
into the problem that "set of A" is not the same logical type as "A".
So you can't translate "Everyone on this list loves Lojban" to "the set
of everyone in this list loves Lojban"; you have to translate it to "for
all X such that X is a member of the set of everyone in this list, X
loves Lojban".

Once you've done that transformation, a Prolog-like logic engine can
reduce "does Matt love Lojban?" to "is Matt is on this list?".

(Note how the word "everyone" is embedded within the sentence "Everyone
on this list loves Lojban" and yet its effect on the logical rephrasing
encompasses the whole sentence; consider, too, how one would rephrase
"Matt loves everyone's native language".  This inside-out effect is the
sort of thing that continuations are very good at formalizing.)