Reducing Query Answering to Satisfiability in Nonmonotonic Logics

We propose a unifying view of negation as failure, integrity constraints, and epistemic queries in nonmonotonic reasoning. Specifically, we study the relationship between satisfiability and logical implication in nonmonotonic logics, showing that, in many nonmonotonic formalisms, it is possible and easy to reduce logical implication to satisfiability. This result not only allows for establishing new complexity results for the satisfiability 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 defining 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.