An ASP Approach for Reasoning on Neural Networks under a Finitely Many-Valued Semantics for Weighted Conditional Knowledge Bases

Weighted knowledge bases for description logics with typicality have been recently considered under a “concept-wise” multipreference semantics (in both the two-valued and fuzzy case), as the basis of a logical semantics of multilayer perceptrons (MLPs). In this paper we consider weighted conditional $\mathcal{ALC}$ knowledge bases with typicality in the finitely many-valued case, through three different semantic constructions. For the boolean fragment $\mathcal{LC}$ of $\mathcal{ALC}$ we exploit answer set programming and asprin for reasoning with the concept-wise multipreference entailment under a $\varphi$ -coherent semantics, suitable to characterize the stationary states of MLPs. As a proof of concept, we experiment the proposed approach for checking properties of trained MLPs.