Abstract
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 non-monotonic formalisms whose idea is to minimize (circumscribe) the extension of given predicates. In this paper we study circumscribed extit{DL-Lite} knowledge bases and show how to compute circumscription of a single predicate (either a concept or a role) in a extit{DL-Lite} extsubscript{bool}$^mathcalH$ 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 dlliteboolh requires the language of $mathcal{ALCHOIQ}$ extended with union or roles, thus is first-order expressible.