Sunday, October 25, 2009

A solution for John

It appears that I've been too pessimistic claiming that I can't assemble the meaning of 'John has two sisters' from the word meanings. Blackburn&Bos have taught me:

John: λv (v JOHN)
has: λsubj λobj (subj (λs (obj s id)))
two: λn λy λv (v (∃S (|S|=2 & ∀x∊S (n x y))))
sisters: λx λy SISTER(x,y)

Let's evaluate:

(two sisters) = λy λv (v (∃S (|S|=2 & ∀x∊S SISTER(x,y))))
(has John) = λobj (obj JOHN id)
((has John) (two sisters)):
   ∃S (|S|=2 & ∀x∊S SISTER(x,JOHN))

Note that this semantics also doesn't assume that John has only 2 sisters, so it really looks like an appropriate one.

So, the applicative text structure is restored in its rights. Although I don't much like this kind of solution, because the semantics of 'has' and 'two' are too dependent of the fact that SISTER predicate takes 2 arguments. I'd have to change them both to express 'John has two dogs', thus making 'two' (and every other numeric quantifier) ambiguous in semantics. But it's still better than nothing.

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