From Query Answering to Satissability in Nonmonotonic Logics

We propose a unifying view of negation as failure, integrity constraints, and epistemic queries in nonmonotonic reasoning. Specii-cally, we study the relationship between satis-ability and logical implication in nonmono-tonic logics, showing that, in many nonmono-tonic formalisms, it is possible and easy to reduce logical implication to satissability. This result not only allows for establishing new complexity results for the satissability problem in nonmonotonic logics, but also establishes a clear relationship between the studies on epistemic queries and integrity constraints in monotonic knowledge bases with the work on negation by default in nonmonotonic reasoning and logic programming. From the perspective of the design of knowledge representation systems, such a reduction allows for deening both a simple method for answering epistemic queries in knowledge bases with nonmonotonic abilities, and a procedure for identifying integrity constraints in the knowledge base, which can be employed for optimizing reasoning in such systems.