Spring 2012 IA165 Combinatory Logic for Computational Semantics by Juyeon Kang
Classwork N°6
due to 30th March 2012
Exercise: “Application of combinators to natural language analysis: Extraction asymmetries”
1. To apply successfully the combinators to natural language analysis, we need to handle
adequately the introduction and elimination rules by beta-reduction defined for each
combinator. Especially, the control of the intro. Rules can appeal to some syntactic tool.
Referring to the given combinatorial rules and types, give the formal semantic analysis
of the following sentences:
CCG types: a. primitive types: S for sentence, NP for noun phrase and proper noun, N for common noun
b. derived types: (S\NP) for intransitive verb (unary), (S\NP)/NP for transitive verb(binary),
(N/N) for adjective, (NP/N) for articles, (S\NP)\(S\NP) for adverb of verb, (N/N)/(N/N) for the
adverb of adjective, etc.
CCG rules:
e1: (y/z)  e2:(x\y) e1:x(NPobj) x:e1  CONJ  x:e2
­­­­­­­­­­­­­­­­­­­­<Bx ­­­­­­­­­­­­­­­<C* ­­­­­­­­­­­­­­­> (> )Φ
(x/z): B e2 e1 y/(y\x):  C* e1 x:   CONJ e1 e2Φ
(a) Anna likes but Manny hates the horror movie. (type of but: CONJ)
(b) I will show to him and give to you an engraving. (type-raised argument)
→ type of will: VP/VP; type of show/give: (VP/PP)/NP; type of to: (PP/NP)
(c) I will show a painting and give a flower to him. (NP-shift)
(d) I will travel to and return from the beautiful city of Dublin (NP shift)
→ type of to/from: (PP/NP)
(e) a sculpture which I will buy today and sell tomorrow (leftward extraction)
→ type of which: (N\N)/(S/NP)