A KLM Perspective on Defeasible Reasoning for Description Logics

Abstract

In this paper we present an approach to defeasible reasoning for the description logic \(\mathcal {ALC}\). The results discussed here are based on work done by Kraus, Lehmann and Magidor (KLM) on defeasible conditionals in the propositional case. We consider versions of a preferential semantics for two forms of defeasible subsumption, and link these semantic constructions formally to KLM-style syntactic properties via representation results. In addition to showing that the semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. With the semantics of the defeasible version of \(\mathcal {ALC}\) in place, we turn to the investigation of an appropriate form of defeasible entailment for this enriched version of \(\mathcal {ALC}\). This investigation includes an algorithm for the computation of a form of defeasible entailment known as rational closure in the propositional case. Importantly, the algorithm relies completely on classical entailment checks and shows that the computational complexity of reasoning over defeasible ontologies is no worse than that of the underlying classical \(\mathcal {ALC}\). Before concluding, we take a brief tour of some existing work on defeasible extensions of \(\mathcal {ALC}\) that go beyond defeasible subsumption.