DECOMPOSING GENERALIZED QUANTIFIERS

This note explains the circumstances under which a type < 1 > quantifier can be decomposed into a type < 1, 1 > quantifier and a set, by fixing the first argument of the former to the latter. The motivation comes from the semantics of Noun Phrases (also called Determiner Phrases) in natural languages, but in this article, I focus on the logical facts. However, my examples are taken among quantifiers appearing in natural languages, and at the end, I sketch two more principled linguistic applications.