Semantics for Reasoning with Contradictory Extended Logic Programs

Extended programs are normal programs extended with classical negation. Because of the classical negation in the head of the rules, an extended logic program can be contradictory. Human reasoning is often based on conflicting evidence and on assumptions which are not always valid. Our goal is to derive useful conclusions from programs that may be contradictory. We consider rules to be defaults. Rule prioritization can be viewed as a tool to specify confidence information about these defaults. We present a new semantics for extended programs with rule prioritization, called contradiction-free semantics (CFS). CFS is defined as the least fixpoint of a monotonic operator. Every extended program with rule prioritization has at least one stable c-model. We show that the CFS of a program P coincides with the least stable c-model of P. A sound and complete proof procedure to answer queries based on CFS is described.