mlsanityData to 7 Oct 2026

A Categorical Semantics of Fuzzy Concepts in Conceptual Spaces

arXiv 2110.05985 ↗First posted 12 Oct 2021math.CT cs.AI cs.LOcited by 4

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Abstract (arXiv)

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.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 9 of its 32 references that are in the map. First posted on arXiv 12 Oct 2021.

Builds on

9 of 32 references.

References · 9

  1. 2016The Concrete Distribution: A Continuous Relaxation of Discrete Random Variablescited by 1,135
  2. 2019A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statisticscited by 55
  3. 2017Disintegration and Bayesian Inversion via String Diagramscited by 32
  4. 2019The Mathematics of Text Structurecited by 24
  5. 2017Interacting Conceptual Spaces I : Grammatical Composition of Conceptscited by 13
  6. 2020Representable Markov Categories and Comparison of Statistical Experiments in Categorical Probabilitycited by 11
  7. 2017A Thorough Formalization of Conceptual Spacescited by 5
  8. 2014Autonomization of Monoidal Categoriescited by 3
  9. 2015A Compositional Explanation of the Pet Fish Phenomenoncited by 3

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Cited by year

Citing papers per year: 2022: 1; 2023: 2; 2024: 1.

4 papers.

  1. 2024Towards Compositional Interpretability for XAIcited by 10
  2. 2022The Conceptual VAEcited by 3
  3. 2023From Conceptual Spaces to Quantum Concepts: Formalising and Learning Structured Conceptual Modelscited by 3
  4. 2023Formalising and Learning a Quantum Model of Conceptscited by 0