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Reasoning in the presence of inconsistency through Preferential ALC

This paper presents an inconsistency tolerant semantics for the Description Logic ALC called Preferential ALC (p-ALC ). A p-ALC knowledge base is comprised of defeasible and non-defeasible axioms. The defeasible ABox and TBox are labelled with confidence weights that could reflect an axiom’s provenance. Entailment is defined through the notion of preferred interpretations which minimise the total weight of the inconsistent axioms. We introduce a modified ALC tableau algorithm in which the open branches give rise to the preferred interpretations, and show that it can compute p-ALC entailment by refutation. The modified algorithm is implemented as an incremental answer set program (ASP) that exploits optimisation to capture preferred interpretations of p-ALC .