{"title":"A Categorical Semantics of Fuzzy Concepts in Conceptual Spaces","authors":"S. Tull","doi":"10.4204/EPTCS.372.22","DOIUrl":null,"url":null,"abstract":"We define a symmetric monoidal category modelling fuzzy concepts and fuzzy conceptual reasoning within G\\\"ardenfors' framework of conceptual (convex) spaces. We propose log-concave functions as models of fuzzy concepts, showing that these are the most general choice satisfying a criterion due to G\\\"ardenfors and which are well-behaved compositionally. We then generalise these to define the category of log-concave probabilistic channels between convex spaces, which allows one to model fuzzy reasoning with noisy inputs, and provides a novel example of a Markov category.","PeriodicalId":11810,"journal":{"name":"essentia law Merchant Shipping Act 1995","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"essentia law Merchant Shipping Act 1995","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4204/EPTCS.372.22","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
Abstract
We define a symmetric monoidal category modelling fuzzy concepts and fuzzy conceptual reasoning within G\"ardenfors' framework of conceptual (convex) spaces. We propose log-concave functions as models of fuzzy concepts, showing that these are the most general choice satisfying a criterion due to G\"ardenfors and which are well-behaved compositionally. We then generalise these to define the category of log-concave probabilistic channels between convex spaces, which allows one to model fuzzy reasoning with noisy inputs, and provides a novel example of a Markov category.
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