Algebras over a field and semantics for context based reasoning

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.