Circumscription: Formalization of Non-monotonic Reasoning in Second Order Logic

Abstract

We discuss circumscription, a logical formalization of non-monotonic reasoning, introduced by John McCarthy and Vladimir Lifschitz. First section contains presentation of assumptions of logic-based artificial intelligence, problem of non-monotonicity in commonsense reasoning and informal formulation of circumscription. In section two, a formal definition of circumscription is given. The idea of circumscription is discussed from syntactic and semantic point of view. Theoretical investigations are supplemented with examples. In section three, methods of computing circumscription are discussed. Section four contains exemplary circumscription-based formalization of simple non-monotonic reasoning. Finally, not only a comment about the role of logic in artificial intelligence is made but a piece of information about implementation of circumscription is given as well.