Formal ways for measuring relations between concepts in conceptual spaces†

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. In this article, we extend our recent mathematical formalization of this framework by providing quantitative mathematical definitions for measuring relations between concepts. We develop formal ways for computing concept size, subsethood, implication, similarity, and betweenness. This considerably increases the representational capabilities of our formalization.

Automated summary

The article extends the mathematical formalization of the conceptual spaces framework by providing quantitative mathematical definitions for measuring relations between concepts, enhancing the representational capabilities of the framework.