On the Equivalence of Semantics for Normal Logic Programs

Despite the frequent comment that there is no general agreement on the semantics of logic programs, this paper shows that a number of independently proposed extensions to the stable model semantics coincide: the regular model semantics proposed by You and Yuan, the partial stable model semantics by Sacc`a and Zaniolo, the preferential semantics by Dung, and a stronger version of the stable class semantics by Baral and Subrahmanian. We show that these equivalent semantics can be characterized simply as selecting a particular kind of stable classes, called normal alternating fixpoints. In addition, we indicate that almost all proposed semantic frameworks coincide with three-valued stable models, or equivalently, with normal alternating fixpoints. Due to its simplicity and naturalness, the framework of alternating fixpoints offers great potential in the study of the semantics for various nonmonotonic systems. 1 Introduction Since the discovery of the stable model semantics for normal lo..