Algebras over a field and semantics for context based reasoning

This chapter introduces context algebras and demonstrates their application to combining logical and vector-based representations of meaning. Other chapters in this volume consider approaches that attempt to reproduce aspects of logical semantics within new frameworks. The approach we present here is different: We show how logical semantics can be embedded within a vector space framework, and use this to combine distributional semantics, in which the meanings of words are represented as vectors, with logical semantics, in which the meaning of a sentence is represented as a logical form. The ideas discussed here are present (at least implicitly) in earlier work, however we have introduced some notions which allow the mathematics to be tidied considerably: