Measuring Relations Between Concepts In Conceptual Spaces

TL;DR

This paper enhances the mathematical formalization of conceptual spaces by defining quantitative measures for concept relations, thereby increasing the framework's ability to represent complex knowledge structures geometrically.

Contribution

It introduces new quantitative definitions for concept size, subsethood, implication, similarity, and betweenness within the conceptual spaces framework.

Findings

Provides measurable ways to describe relations between concepts.

Increases the representational power of conceptual spaces.

Formalizes geometric notions of concept relations.

Abstract

The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by regions in this space. Our recent mathematical formalization of this framework is capable of representing correlations between different domains in a geometric way. In this paper, we extend our formalization by providing quantitative mathematical definitions for the notions of concept size, subsethood, implication, similarity, and betweenness. This considerably increases the representational power of our formalization by introducing measurable ways of describing relations between concepts.