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

In this paper we establish a link between fuzzy and preferential semantics for description logics and self-organizing maps (SOMs), which have been proposed as possible candidates to explain the psychological mechanisms underlying category generalization. In particular, we show that the input/output behavior of a SOM 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.