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

• URL: http://arxiv.org/abs/2303.04534v2
• Date: Mon, 27 Mar 2023 17:12:47 GMT
• Title: Complexity and scalability of defeasible reasoning in many-valued weighted knowledge bases with typicality
• Authors: Mario Alviano, Laura Giordano, Daniele Theseider Dupr\'e
• Abstract summary: Weighted knowledge bases for description logics with typicality provide a logical interpretation of MultiLayer Perceptrons. ASP has been shown to be suitable for addressing defeasible reasoning in the finitely many-valued case. This paper provides a $PNP[log]$-completeness result and new ASP encodings that deal with weighted knowledge bases with large search spaces.
• Score: 4.447467536572624
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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