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

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 fulfills the lack by providing a ${P<^>{NP[log]}}$-completeness result and new ASP encodings that deal with both acyclic and cyclic weighted knowledge bases with large search spaces, as assessed empirically on synthetic test cases. The encodings are used to empower a reasoner for computing solutions and answering queries, possibly interacting with ASP Chef for obtaining an interactive visualization.