A conditional, a fuzzy and a probabilistic interpretation of self-organising maps
Abstract
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.
Keywords
Cite
@article{arxiv.2103.06854,
title = {A conditional, a fuzzy and a probabilistic interpretation of self-organising maps},
author = {Laura Giordano and Valentina Gliozzi and Daniele Theseider Dupré},
journal= {arXiv preprint arXiv:2103.06854},
year = {2022}
}
Comments
31 pages, 1 figure. arXiv admin note: text overlap with arXiv:2008.13278