5 votes

logic symbol for 'unlike, differing from'

(Why is there still no MathJax support for this SE?! Googling and copy-pasting unicode symbols every time you want to talk about semantics is really annoying.) What you want to say is basically ¬φ(a)...
Natalie Clarius's user avatar
3 votes
Accepted

Should λ-terms all be easily translated back into natural language syntax?

(a) is the denotation for gray proposed in (11) on p. 66. Its type is (et)et so that when applied to cat with type et we get gray cat with type et as well. In (b) we have a predicate f of which Ann is ...
Keelan's user avatar
  • 4,136
2 votes
Accepted

Gapping in Lambda Expressions?

I suppose you mean something like (1b) and (2b), for (1a) and (2a), respectively: (1) a. John bought and Bill cooked the turkey. b. [λx . ⟦bought⟧(x)(⟦John⟧) ∧ ⟦cooked⟧(x)⟦Bill⟧](⟦the turkey⟧) ...
Brian Buccola's user avatar
2 votes
Accepted

The determiner "a" in lambda form

Perhaps "a" is an ambiguous reduced form derived from either (any) or (some). Thus "A man loves Mary" could be from either "Any man loves Mary" or "Some man loves Mary". Note the ambiguity of "Mary ...
Greg Lee's user avatar
  • 12.5k
2 votes

What is the best/state-of-the-art logic for representing English language?

The wording of your question seems to imply an equivalence between first order predicate logic and higher order logics. They are not equivalent. First order predicate logic was shown to be ...
Greg Lee's user avatar
  • 12.5k
2 votes

Parsing with CCGs - lambda part

I'll leave the lambdas to you, but you might like to know the syntactic structure. It is a RNR (right node-raising) construction, with "pillow" the raised node. The intonation I think makes that ...
Greg Lee's user avatar
  • 12.5k
1 vote
Accepted

Parsing with CCGs - lambda part

square = λf.λx.f(x) ^ square(x) blue = λg.λy.g(y) ^ blue(y) square ° blue (1) = λh.square(blue(h)) (2) = λh.[λf.λx.f(x) ^ square(x)]([λg.λy.g(y) ^ blue(y)](h)) (3) = λh.[λf.λx.f(x) ^ square(x)](λy.h(...
David Vogt's user avatar
1 vote

Parsing with CCGs - lambda part

Your computation is correct, and the video simply shows the wrong result. The order square(x) ^ blue(x) comes from the fact that squared is applied to blue where blue will be substituted for f in the ...
Natalie Clarius's user avatar
1 vote

Converting types into lambda notation and set notation

As for and: You got your lambda term for and wrong. Either you mean coordination between subject DPs ("Mary and John sneeze") then your lambda term is λP[λx[λy[P(x)^P(y)]]], with just one ...
Natalie Clarius's user avatar
1 vote

What is the best/state-of-the-art logic for representing English language?

I'd recommend looking at Jerry Hobbs' way of parsing and representing English, it's one of the most elaborate ones when it comes to logic and commonsense representation: Jerry Hobbs: "Discourse and ...
Atamiri's user avatar
  • 2,590
1 vote

Representing prepositions in lambda calculus/logic notation

Just from this example it would seem that the type of for is ((e,t),t), ((e,t),(e,t)) -- because it combines with a DP to make up an adjunct to the VP. Thus, it could have a semantics like the ...
Ivan Kapitonov's user avatar

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