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.