Polynomial Event Semantics: Non-Montagovian Proper Treatment of Quantifiers

摘要

We propose a simple extension of event semantics that naturally supports the compositional treatment of quantification. Our analyses require neither quantifier raising or other syntactic movements, nor type-lifting. Denotations are computed strictly compositionally, from lexical entries up, and quantifiers are analyzed in situ. We account for the universal, existential and counting quantification and the related distributive coordination, with the attendant quantifier ambiguity phenomena. The underlying machinery is not of lambda-calculus but of much simpler relational algebra, with straightforward set-theoretic interpretation. The source of quantifier ambiguity in our approach lies in two possible analyses for the existential (and counting) quantification. Their inherent ambiguity however becomes apparent only in the presence of another, non-existential quantification.