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arXiv · 2303.04534

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

Mario Alviano·Laura Giordano·Daniele Theseider Dupré
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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.

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Mario Alviano, Laura Giordano, Daniele Theseider Dupré. 2023-03-08. Complexity and scalability of defeasible reasoning in many-valued weighted knowledge bases with typicality. https://arxiv.org/abs/2303.04534

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