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

arXiv: https://arxiv.org/abs/2103.06854 · HTML: https://mlsanity.com/paper/2103.06854/

## 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 (most cited first, 13 of 13)

- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoning](https://mlsanity.com/paper/1905.06088/) (2019)
- [Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective](https://mlsanity.com/paper/2003.00330/) (2020)
- [Thinking Fast and Slow: Optimization Decomposition Across Timescales](https://mlsanity.com/paper/1704.07785/) (2017)
- [Ontology Reasoning with Deep Neural Networks](https://mlsanity.com/paper/1808.07980/) (2018)
- [An ASP approach for reasoning in a concept-aware multipreferential lightweight DL](https://mlsanity.com/paper/2006.04387/) (2020)
- [Weighted defeasible knowledge bases and a multipreference semantics for a deep neural network model](https://mlsanity.com/paper/2012.13421/) (2020)
- [A Polynomial Time Subsumption Algorithm for Nominal Safe ELO_bot under Rational Closure](https://mlsanity.com/paper/1802.08201/) (2018)
- [On a plausible concept-wise multipreference semantics and its relations with self-organising maps](https://mlsanity.com/paper/2008.13278/) (2020)
- [A framework for a modular multi-concept lexicographic closure semantics](https://mlsanity.com/paper/2009.00964/) (2020)
- [Revision by Conditionals: From Hook to Arrow](https://mlsanity.com/paper/2006.15811/) (2020)

## Built on by (most cited first, 6 of 6)

- [On the KLM properties of a fuzzy DL with Typicality](https://mlsanity.com/paper/2106.00390/) (2021)
- [An ASP approach for reasoning on neural networks under a finitely many-valued semantics for weighted conditional knowledge bases](https://mlsanity.com/paper/2202.01123/) (2022)
- [From Weighted Conditionals of Multilayer Perceptrons to Gradual Argumentation and Back](https://mlsanity.com/paper/2110.03643/) (2021)
- [Many-valued Argumentation, Conditionals and a Probabilistic Semantics for Gradual Argumentation](https://mlsanity.com/paper/2212.07523/) (2022)
- [A preferential interpretation of MultiLayer Perceptrons in a conditional logic with typicality](https://mlsanity.com/paper/2305.00304/) (2023)
- [From Common Sense Reasoning to Neural Network Models through Multiple Preferences: an overview](https://mlsanity.com/paper/2107.04870/) (2021)

## 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.