  In this paper we discuss the relationships between conditional and
preferential logics and neural network models, based on a multi-preferential
semantics. We propose a concept-wise multipreference semantics, recently
introduced for defeasible description logics to take into account preferences
with respect to different concepts, as a tool for providing a semantic
interpretation to neural network models. This approach has been explored both
for unsupervised neural network models (Self-Organising Maps) and for
supervised ones (Multilayer Perceptrons), and we expect that the same approach
might be extended to other neural network models. It allows for logical
properties of the network to be checked (by model checking) over an
interpretation capturing the input-output behavior of the network. For
Multilayer Perceptrons, the deep network itself can be regarded as a
conditional knowledge base, in which synaptic connections correspond to
weighted conditionals. The paper describes the general approach, through the
cases of Self-Organising Maps and Multilayer Perceptrons, and discusses some
open issues and perspectives.

Artificial Intelligence