Complexity and Scalability of Defeasible Reasoning with Typicality in Many-Valued Weighted Knowledge Bases

Mario Alviano, Laura Giordano, Daniele Theseider Dupré

Abstract: Weighted knowledge bases for description logics with typicality under a “concept-wise” multi-preferential semantics provide a logical interpretation of MultiLayer Perceptrons. In this context, Answer Set Programming (ASP) has been shown to be suitable for addressing defeasible reasoning in the finitely many-valued case, providing a \(\varPi ^p_2\) upper bound on the complexity of the problem, nonetheless leaving unknown the exact complexity and only providing a proof-of-concept implementation. This paper fulfils the lack by providing a \({P^{NP[log]}}\)-completeness result and new ASP encodings that deal with weighted knowledge bases with large search spaces.