Circumscribing DL-Lite

Classical logics (and hence Description Logics) are monotonic: the set of conclusions increases monotonically with the set of premises. Instead, common-sense reasoning is characterized as non-monotonic: new information can invalidate some of the previously made conclusions. Circumscription is one of the main nonmonotonic formalisms whose idea is to minimize (circumscribe) the extension of given predicates. In this paper we study circumscribed DL-Lite knowledge bases and show how to compute circumscription of a single predicate (either a concept or a role) in a DL-LiteH bool knowledge base. Unlike other works on circumscribed Description Logics KBs, we are interested not only in checking entailment, but actually in computing circumscription itself. We show that circumscription of a role in DL-LiteH bool requires the language of ALCHOIQ extended with union or roles, thus is first-order expressible.