  This paper introduces context algebras and demonstrates their application to
combining logical and vector-based representations of meaning. Other approaches
to this problem 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.
