An ASP approach for reasoning on neural networks under a finitely many-valued semantics for weighted conditional knowledge bases
This work provides a logical framework for verifying neural networks, but it is incremental as it builds on existing multipreference semantics for description logics.
The paper tackles the problem of reasoning about weighted conditional knowledge bases with typicality under a finitely many-valued semantics, proposing an Answer Set Programming (ASP) approach to check properties of trained MultiLayer Perceptrons (MLPs).
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 ALC knowledge bases with typicality in the finitely many-valued case, through three different semantic constructions. For the boolean fragment LC of ALC we exploit ASP and "asprin" for reasoning with the concept-wise multipreference entailment under a phi-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. The paper is under consideration for acceptance in TPLP.