Nonmonotonicity and answer set inference

Abstract

The study of abstract properties of nonmonotonic inference has thrown up a number of general conditions on inference relations that are often thought to be desirable, and sometimes even essential, for an adequate system of nonmonotonic reasoning. However, several of the key conditions on inference that have been proposed in the literature make explicit reference to the classical concept of logical consequence, and there is a general tendency to focus attention on inference operations that are supraclassical in the sense of extending classical consequence. Against this trend I argue for the importance of systems that are not supraclassical. I suggest that their inference relations should measure up to adequacy conditions that are more sensitive to the style of reasoning for which they are intended, and which take account of the underlying logic of the monotonic subsystem, if such a subsystem can be identified. I illustrate these points by considering some properties of the inference relation associated with the answer set semantics of extended disjunctive databases.