Formal Ways for Measuring Relations between Concepts in Conceptual Spaces
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. 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.
Keywords
Cite
@article{arxiv.1804.02393,
title = {Formal Ways for Measuring Relations between Concepts in Conceptual Spaces},
author = {Lucas Bechberger and Kai-Uwe Kühnberger},
journal= {arXiv preprint arXiv:1804.02393},
year = {2018}
}
Comments
Submitted to a special issue of the Journal "Expert Systems" (https://onlinelibrary.wiley.com/journal/14680394). arXiv admin note: substantial text overlap with arXiv:1707.02292, arXiv:1801.03929, arXiv:1707.05165, arXiv:1708.05263, arXiv:1706.06366