Three-valued nonmonotonic formalisms and semantics of logic programs

Abstract

We introduce three-valued extensions of major nonmonotonic formalisms and we prove that the recently proposed well-founded semantics of logic programs is equivalent, for arbitrary logic programs, to three-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 justification of the well-founded semantics as a natural extension of the perfect model semantics from the class of stratified 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 nonmonotonic formalisms coincide. It also paves the way for using efficient computation methods, developed for logic programming, as inference mechanisms for nonmonotonic reasoning.