Weighted knowledge bases with typicality and defeasible reasoning in a gradual argumentation semantics

Abstract

Weighted knowledge bases for description logics with typicality provide a logical interpretation of MultiLayer Perceptrons, based on a “concept-wise” multi-preferential semantics. On the one hand, in the finitely many-valued case, Answer Set Programming (ASP) has been shown to be suitable for addressing defeasible reasoning from weighted knowledge bases for the boolean fragment of ALC . On the other hand, the semantics of weighted knowledge bases with typicality, in their different variants, have suggested some new gradual argumentation semantics, as well as an approach for defeasible reasoning over a weighted argumentation graph, building on the gradual semantics and, specifically on the φ-coherent semantics. In this paper, we explore the relationships between weighted knowledge bases and weighted argumentation graphs, to develop proof methods for defeasible reasoning over an argumentation graph under the φ-coherent semantics, in the finitely-valued case. We establish a mapping from a weighted argumentation graph to a weighted knowledge base as well as a lower bound on the complexity of the problem of verifying graded implications over an argumentation graph in the φ-coherent semantics. We also consider a mapping from weighted knowledge bases to weighted argumentation graphs, and provide an ASP implementation and some experimental results.