Nonmonotonic Reasoning in Description Logic by Tableaux Algorithm with Blocking

Abstract. To support nonmonotonic reasoning we introduce the description logic of minimal knowledge and negation as failure (MKNF-DL) as an extension of description logic with modal operators K and A. We discuss the problems with representation of a model for an MKNF-DL theory. For satisfiability checking of MKNF-DL theories, we introduce a tableaux algorithm with blocking, where blocking works with the modal part of an MKNF-DL theory. This blocking technique allows for reasoning about a larger class of MKNF-DL theories than previous approaches. Recently, Description Logics (DL) are used to represent and reason about knowledge bases (KBs). In practical applications, the monotonic property of standard logics, which includes DLs, may be undesirable. Hence, we introduce ALCKN F, the DL of minimal knowledge and negation as failure (MKNF-DL) as an extension of description logic (DL) with modal operators K and A. Advanced reasoning applications, including epistemic queries, integrity constraints and default rules can be represented by ALCKN F [4]. Next, we introduce a reasoning technique for ALCKN F. To this end the representation of ALCKN F models is crucial. The models of ALCKN F are not first-order representable. Hence, we define subjectively quantified KBs which are representable by ALC theory. However, this ALC theory may be infinite. Previous approaches [1, 3] defined simple KBs, a subset of subjectively quantified KBs, which are representable by finite ALC theory. The intention of our research was an effective reasoning method for subjectively quantified KB. We achieved this by introducing a tableaux algorithm with blocking; however, for the algorithm to be complete, a further restriction to minimality-proper KBs is neccessary. Still, minimality-proper KBs include simple KBs