Measuring Relations Between Concepts In Conceptual Spaces
This work addresses the need for measurable descriptions of concept relations in knowledge representation, but it appears incremental as it builds on their previous formalization.
The paper tackles the problem of quantifying relations between concepts in conceptual spaces by providing mathematical definitions for size, subsethood, implication, similarity, and betweenness, which enhances the representational power of their formalization.
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.