Generalized Quantifiers in Compositional Distributional Semantics

Based on the work of logicians such as Sgro and Keisler, Barwise and Perry argue that first order logic quantifiers are extremely atypical both in mathematics and in linguistics. They argue that typical quantification should depend on the properties of the underlying model rather than being defined in general and independently. This methodology becomes very handy when defining quantifiers for non-standard models such as vector spaces (that do not easily lend themselves to a traditional notion of logic). So, in this talk, I will present recent work and show how one may do this for distributional models. I will use previous work (joint with Clark and Coecke) on relative pronouns and Frobenius algebras to derive the syntactic types and categorical semantics and use these to compose the vectors of the words in quantified phrases and sentences. A theoretical justification is provided via an analogy with sets and relations. Experimentation is left to future work.