A Compositional Analysis of Anti-Quantifiers as Quantifiers

Quantifiers ∗

Quantifiers are terms of generality. They are also among our prime examples of operators which take scope. The distinction between singular and general terms, as well as the ways that general terms enter into scope relations, are certainly fundamental to our understanding of language. Yet when we turn to natural language, we encounter a huge and apparently messy collection of general terms; not...

Weak Quantifiers

Generalized Quantifiers

We review recent work in the field of generalized quantifiers on finite models. We give an idea of the methods that are available in this area. Main emphasis is on definability issues, such as whether there is a logic for the PTIME properties of unordered finite models.

Encoding Generalized Quantifiers in Dependency-based Compositional Semantics

For textual entailment recognition systems, it is often important to correctly handle Generalized quantifiers (GQ). In this paper, we explore ways of encoding GQs in a recent framework of Dependency-based Compositional Semantics, especially aiming to correctly handle linguistic knowledge like hyponymy when GQs are involved. We use both the selection operator mechanism and a new relation extensi...

Modular quantifiers

In the late nineteen-eighties much of our research concerned the application of semigroup-theoretic methods to automata and regular languages, and the connection between computational complexity and this algebraic theory of automata. It was during this period that we became aware of the work of Wolfgang Thomas. Thomas had undertaken the study of concatenation hierarchies of star-free regular la...