A Context-theoretic Framework for Compositionality in Distributional Semantics

TL;DR

This paper introduces a formal framework for compositional distributional semantics where words, phrases, and sentences are represented as vectors, grounded in context and algebraic structures, unifying and generalizing existing vector composition methods.

Contribution

It provides a novel theoretical framework linking vector space models with formal semantics, incorporating algebraic and lattice structures to model meaning and entailment.

Findings

Vectors form an algebra over a field for representing meanings.

Lattice structure models entailment between meanings.

Framework generalizes existing vector composition methods.

Abstract

Techniques in which words are represented as vectors have proved useful in many applications in computational linguistics, however there is currently no general semantic formalism for representing meaning in terms of vectors. We present a framework for natural language semantics in which words, phrases and sentences are all represented as vectors, based on a theoretical analysis which assumes that meaning is determined by context. In the theoretical analysis, we define a corpus model as a mathematical abstraction of a text corpus. The meaning of a string of words is assumed to be a vector representing the contexts in which it occurs in the corpus model. Based on this assumption, we can show that the vector representations of words can be considered as elements of an algebra over a field. We note that in applications of vector spaces to representing meanings of words there is an underlying lattice structure; we interpret the partial ordering of the lattice as describing entailment between meanings. We also define the context-theoretic probability of a string, and, based on this and the lattice structure, a degree of entailment between strings. We relate the framework to existing methods of composing vector-based representations of meaning, and show that our approach generalises many of these, including vector addition, component-wise multiplication, and the tensor product.