Spring 2012 IA165 Combinatory Logic for Computational Semantics by Juyeon Kang
Classwork N°11
due to 11th May 2012
Exercise: “Application of combinators to natural language analysis: Quantification”
1. Universal and existential quantifiers
Please represent the following sentences using the operators of the universal or
existential quantification. Are there ambiguous sentences having more than one reading?
a) All cats are mammals.
b) Some cats were sleeping by the fire.
c) Some chairs are in the lounge.
d) Every man loves a woman.
e) A boy kissed every girl.
2. Formal semantic analysis of the quantifiers
Give the analysis of the following sentences which contain the quantifiers using the
combinators. The illative quantifiers Π2 and Σ2 are defined in term of the combinators.
f) Some girl likes Fred
g) Every boy admires a saxophonist (ambiguous)
h) Every man knows Dexter
i) Several girls carried a box (ambiguous)
[ Σ2
 =def
 (B(CB2
)Φ) & Σ1
 ][ Π2
 =def
 ((B(CB2
) ) => Φ Π1
) ]
Every: (∀x)[P(x) =>Q(x)]
Some: (∃x)[P(x) & Q(x)]
Every:  (λP.λQ((∀x)[P(x) => Q(x)]))
Some:   (λP.λQ((∃x)[P(x) & Q(x)]))