{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/formal-ways-for-measuring-relations-between","title":"Formal Ways for Measuring Relations between Concepts in Conceptual Spaces","arxiv_id":"1804.02393","date":"2018-04-06","proceeding":null,"authors":["Lucas Bechberger","Kai-Uwe Kühnberger"],"abstract":"The highly influential framework of conceptual spaces provides a geometric\nway of representing knowledge. Instances are represented by points in a\nhigh-dimensional space and concepts are represented by regions in this space.\nIn this article, we extend our recent mathematical formalization of this\nframework by providing quantitative mathematical definitions for measuring\nrelations between concepts: We develop formal ways for computing concept size,\nsubsethood, implication, similarity, and betweenness. This considerably\nincreases the representational capabilities of our formalization and makes it\nthe most thorough and comprehensive formalization of conceptual spaces\ndeveloped so far.","url_abs":"http://arxiv.org/abs/1804.02393v1","url_pdf":"http://arxiv.org/pdf/1804.02393v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"formal-ways-for-measuring-relations-between","repo_url":"https://github.com/lbechberger/ConceptualSpaces","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}