A Categorical Semantics of Fuzzy Concepts in Conceptual Spaces
Category Theory
2022-11-04 v2 Artificial Intelligence
Logic in Computer Science
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.
Keywords
Cite
@article{arxiv.2110.05985,
title = {A Categorical Semantics of Fuzzy Concepts in Conceptual Spaces},
author = {Sean Tull},
journal= {arXiv preprint arXiv:2110.05985},
year = {2022}
}
Comments
In Proceedings ACT 2021, arXiv:2211.01102