mlsanityData to 14 Oct 2026

A conditional, a fuzzy and a probabilistic interpretation of self-organising maps

arXiv 2103.06854 ↗First posted 11 Mar 2021cs.AIcited by 6

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Abstract (arXiv)

In this paper we establish a link between fuzzy and preferential semantics for description logics and Self-Organising Maps, which have been proposed as possible candidates to explain the psychological mechanisms underlying category generalisation. In particular, we show that the input/output behavior of a Self-Organising Map after training can be described by a fuzzy description logic interpretation as well as by a preferential interpretation, based on a concept-wise multipreference semantics, which takes into account preferences with respect to different concepts and has been recently proposed for ranked and for weighted defeasible description logics. Properties of the network can be proven by model checking on the fuzzy or on the preferential interpretation. Starting from the fuzzy interpretation, we also provide a probabilistic account for this neural network model.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 13 of its 107 references that are in the map. First posted on arXiv 11 Mar 2021.

Builds on

13 of 107 references.

References · 13

  1. 2019Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AIcited by 1,552
  2. 2018A Survey Of Methods For Explaining Black Box Modelscited by 973
  3. 2019Neural Probabilistic Logic Programming in DeepProbLogcited by 394
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  10. 2018A Polynomial Time Subsumption Algorithm for Nominal Safe ELO_bot under Rational Closurecited by 8
  11. 2020On a plausible concept-wise multipreference semantics and its relations with self-organising mapscited by 5
  12. 2020A framework for a modular multi-concept lexicographic closure semanticscited by 5
1 more
  1. 2020Revision by Conditionals: From Hook to Arrowcited by 2

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Cited by year

Citing papers per year: 2021: 3; 2022: 2; 2023: 1.

6 papers.

  1. 2021On the KLM properties of a fuzzy DL with Typicalitycited by 6
  2. 2022An ASP approach for reasoning on neural networks under a finitely many-valued semantics for weighted conditional knowledge basescited by 4
  3. 2021From Weighted Conditionals of Multilayer Perceptrons to Gradual Argumentation and Backcited by 1
  4. 2022Many-valued Argumentation, Conditionals and a Probabilistic Semantics for Gradual Argumentationcited by 1
  5. 2023A preferential interpretation of MultiLayer Perceptrons in a conditional logic with typicalitycited by 1
  6. 2021From Common Sense Reasoning to Neural Network Models through Multiple Preferences: an overviewcited by 0