Complexity and scalability of defeasible reasoning in many-valued weighted knowledge bases with typicality

TL;DR

This paper investigates the complexity of defeasible reasoning in many-valued weighted knowledge bases with typicality, providing new complexity results and ASP encodings to handle large search spaces effectively.

Contribution

It establishes a $P^{NP[log]}$-completeness result and introduces new ASP encodings for weighted knowledge bases with large search spaces.

Findings

Proves $P^{NP[log]}$-completeness for the problem

Develops new ASP encodings for large search spaces

Addresses complexity and scalability in defeasible reasoning

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 $\Pi^p_2$ 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.