An ASP approach for reasoning on neural networks under a finitely many-valued semantics for weighted conditional knowledge bases

TL;DR

This paper introduces an ASP-based reasoning approach for weighted conditional knowledge bases with finitely many truth values, aiming to analyze properties of trained neural networks modeled as MultiLayer Perceptrons.

Contribution

It develops three semantic constructions for weighted conditional ALC knowledge bases with typicality in the finitely many-valued setting, integrating ASP and asprin for reasoning.

Findings

Successfully reasoned about properties of trained MLPs

Proposed a novel ASP-based reasoning framework for finitely-valued semantics

Validated the approach through experimental checks on neural network properties

Abstract

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.