Three-Valued Non-Monotonic Formalisms and Semantics of Logic Programs

We introduce 3-valued extensions of major non-monotonic formalisms and we prove that the recently proposed well-founded semantics of logic programs is equivalent, for arbitrary logic programs, to 3-valued forms of McCarthy's circumscription, Reiter's closed world assumption, Moore's autoepistemic logic and Reiter's default theory. This result not only provides a further justiication of the well-founded semantics , as a natural extension of the perfect model semantics from the class of stratiied programs to the class of all logic programs, but it also establishes the class of all logic programs as a large class of theories, for which natural forms of all four non-monotonic formalisms coincide. It also paves the way for using eecient computation methods, developed for logic programming, as inference mechanisms for non-monotonic reasoning.