A CLASSIFICATION THEORY OF SEMANTICS OF NORMAL LOGIC PROGRAMS: II. WEAK PROPERTIES

Abstract

Our aim in this article is to supplement the set of strong properties introduced in the preceding article ([Dix94]) with a set of weak principles in order to characterize semantics of logic programs. In [Dix94] we introduced our point of view: we observed that all semantics induce in a natural way a sceptical non-monotonic entailment relation SEM^scept. We ask for the properties of these sceptical relations and use them to describe all possible semantics. We collect in this paper serious shortcomings of some semantics proposed recently. Their strange behaviour led us to formulate in a natural way certain principles to avoid these problems. We argue that any well-behaved semantics should satisfy these principles. The main results state that our list of weak principles is complete in the following sense: any well-behaved-semantics is an extension of the well-founded semantics WFS and coincides for stratified programs with Apt, Blair, and Walker's supported model M^supp_P. We also claim that two extensions of the well-founded semantics (introduced in the preceding article) are uniquely characterized by their strong and weak properties.