Non-monotonic reasoning with logic programming

Our purpose is to exhibit a modular systematic method of representing non-monotonic reasoning problems with the Well-Founded Semantics WFS of extended logic programs augmented with eXplicit negation (WFSX), augmented by its Contradiction Removal Semantics (CRSX) when needed. We apply this semantics, and its contradiction removal semantics counterpart, to represent non-monotonic reasoning problems. We show how to cast in the language of logic programs extended with explicit negation such forms of non-monotonic reasoning as defeasible reasoning, abductive reasoning, and hypothetical reasoning and apply them to such different domains of knowledge representation as hierarchies and reasoning about actions. We then abstract a modular systematic method of representing non-monotonic problems in a logic programming semantics comprising two forms of negation avoiding some drawbacks of other proposals, with which we relate our work.