Relevant Closure: A New Form of Defeasible Reasoning for Description Logics

Among the various proposals for defeasible reasoning for description logics, rational closure, a procedure originally defined for propositional logic, turns out to have a number of desirable properties. Not only it is computationally feasible, but it can also be implemented using existing classical reasoners. One of its drawbacks is that it can be seen as too weak from the inferential point of view. To overcome this limitation we introduce in this paper two extensions of rational closure: basic relevant closure and minimal relevant closure. As the names suggest, both rely on defining a version of relevance. Our formalisation of relevance in this context is based on the notion of a justification (a minimal subset of sentences implying a given sentence). This is, to our knowledge, the first proposal for defining defeasibility in terms of justifications—a notion that is well-established in the area of ontology debugging. Both basic and minimal relevant closure increase the inferential power of rational closure, giving back intuitive conclusions that cannot be obtained from rational closure. We analyse the properties and present algorithms for both basic and minimal relevant closure, and provide experimental results for both basic relevant closure and minimal relevant closure, comparing it with rational closure.