Tags:beta reduction, categorial grammar, head normal form, linear lambda term, Montague semantics and typed lambda calculus

Abstract:

A natural question in categorial grammar is the relation between a syntactic analysis s and the logical form, i.e. the logical formula obtained from this syntactic analysis, once provided with semantic lambda terms. More precisely, do different syntactic analyses fed with equal semantic terms, lead to equal logical form? We shall show that when this question is too simply formulated, the answer is "NO" while with some constraints on semantic lambda terms the answer is "yes".

Do different syntactic trees yield different logical readings? Some remarks on head variables in typed lambda calculus.