Interacting Conceptual Spaces I : Grammatical Composition of Concepts

TL;DR

This paper extends the categorical compositional approach from natural language processing to conceptual spaces in cognition, introducing convex relations and demonstrating how concepts combine to form meanings of complex phrases.

Contribution

It introduces convex relations as a new framework for compositional semantics in cognition and shows how to construct and combine conceptual spaces for different word types.

Findings

Convex relations effectively model conceptual spaces.

Concepts can be systematically combined to derive meanings of complex phrases.

Provides a mathematical foundation for compositional cognition.

Abstract

The categorical compositional approach to meaning has been successfully applied in natural language processing, outperforming other models in mainstream empirical language processing tasks. We show how this approach can be generalized to conceptual space models of cognition. In order to do this, first we introduce the category of convex relations as a new setting for categorical compositional semantics, emphasizing the convex structure important to conceptual space applications. We then show how to construct conceptual spaces for various types such as nouns, adjectives and verbs. Finally we show by means of examples how concepts can be systematically combined to establish the meanings of composite phrases from the meanings of their constituent parts. This provides the mathematical underpinnings of a new compositional approach to cognition.