Rationality and Context in Defeasible Subsumption

Description logics have been extended in a number of ways to support defeasible reasoning in the KLM tradition. Such features include preferential or rational defeasible concept subsumption, and defeasible roles in complex concept descriptions. Semantically, defeasible subsumption is obtained by means of a preference order on objects, while defeasible roles are obtained by adding a preference order to role interpretations. In this paper, we address an important limitation in defeasible extensions of description logics, namely the restriction in the semantics of defeasible concept subsumption to a single preference order on objects. We do this by inducing a modular preference order on objects from each preference order on roles, and use these to relativise defeasible subsumption. This yields a notion of contextualised rational defeasible subsumption, with contexts described by roles. We also provide a semantic construction for and a method for the computation of contextual rational closure, and present a correspondence result between the two.

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