Formal Ways for Measuring Relations between Concepts in Conceptual Spaces
This work addresses the need for more precise representational capabilities in conceptual spaces, a geometric knowledge representation framework, though it appears incremental as an extension of their prior formalization.
The authors tackled the problem of quantifying relationships between concepts in conceptual spaces by developing mathematical definitions for measuring concept size, subsethood, implication, similarity, and betweenness, which they claim makes their formalization the most thorough and comprehensive to date.
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 and makes it the most thorough and comprehensive formalization of conceptual spaces developed so far.