Characterizations of the stable semantics by partial evaluation

Abstract

There are three most prominent semantics defined for certain subclasses of disjunctive logic programs: GCWA (for positive programs), PERFECT (for stratified programs) and STABLE (defined for the whole class of all disjunctive programs). While there are various competitors based on 3-valued models, notably WFS and its disjunctive counterparts, there are no other semantics consisting of 2-valued models. We argue that the reason for this is the Partial Evaluation-property (also called Unfolding or Partial Deduction) wellknown from Logic Programming. In fact, we prove characterizations of these semantics and show that if a semantics SEM satisfies Partial Evaluation and Elimination of Taulologies then (1) SEM is based on 2-volued minimal models for positive programs, and (2) if SEM satisfies in addition Elimination of Contradictions, it is based on stable models. We also show that if we require Isomorphy and Relevance then STABLE is completely determined on the class of all stratified disjunctive logic programs. The underlying notion of a semantics is very general and our abstract properties state that certain syntactical transformations on programs are equivalence preserving.