Algebras over a field and semantics for context based reasoning
Daoud Clarke

TL;DR
This paper presents a novel framework called context algebras that embeds logical semantics into vector spaces, enabling the integration of distributional and logical semantics for richer meaning representation.
Contribution
It introduces context algebras as a new method to combine logical and vector-based semantics within a unified mathematical framework.
Findings
Successfully embeds logical semantics into vector spaces
Demonstrates combining distributional and logical semantics
Provides a new approach to meaning representation
Abstract
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.
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