A conditional, a fuzzy and a probabilistic interpretation of self-organising maps
This work offers a theoretical interpretation for neural network models in cognitive science, but it is incremental as it builds on existing semantics without new empirical results.
The paper establishes a formal link between Self-Organising Maps (SOMs) and fuzzy/preferential semantics in description logics, showing that SOM behavior can be described by fuzzy and preferential interpretations, and provides a probabilistic account for the model.
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.