Quantification and Computation
Course Description: Description: Generalized quantifier theory studies the semantics of quantifier expressions, like, `every’, `some’, `most’, ‘infinitely many’, `uncountably many’, etc. The classical version was developed in the 1980s, at the interface of linguistics, mathematics, and philosophy. Generalized quantifiers turned out to be one of the crucial notions in the development of formal semantics but also logic, theoretical computer science and philosophy.
The course gives an introduction to the generalized quantifier theory, overviewing some crucial notions of formal semantics and logic. We survey how mathematical methods may be rigorously applied to study the possible meanings, the inferential power, and computational properties of quantifier expressions. The course novelty lies mostly in combining classical generalized quantifier themes with a computational perspective. Among others, we will discuss universal properties of natural language quantifiers, computational devices recognizing quantifier meanings, learnability theory for quantifiers, and complexity and definability results in generalized quantifier theory.