A New Semantics for Logic Programs Capturing and Extending the Stable Model Semantics

Abstract

Many research works had been done in order to define a semantics for logic programs. Most of these semantics are iterated fixed point semantics. The main idea is the canonical model approach which is a declarative semantics for logic programs that can be defined by selecting for each program one of its canonical models. The notion of canonical models of a logic program is what it is called the stable models. The stable models of a logic program are the minimal Her brand models of its "reduct" programs. The work that we describe in this paper is theoretical, we introduce a new semantics for logic programs that is different from the known fixed point semantics. In our approach, logic programs are expressed as CNF formulas (sets of clauses) of a propositional logic for which we define a notion of extension. We prove in this semantics, that each consistent CNF formula admits at least an extension and for each given stable model of a logic program there exists an extension of its corresponding CNF formula which logically entails it. On the other hand, we show that some of the extensions do not entail any stable model, in this case, we define a simple condition called a discrimination condition which allows to recognize such extensions. These extensions could be very important, but are not captured by the stable models semantics. Our approach, extends the stable model semantics in this sense. Following the new semantics, we give a full characterization of the stable models of a logic program by means of the extensions of its CNF encoding verifying the simple discrimination condition, and provide a procedure which can be used to compute such extensions from which we deduce the stable models and eventually the extra-stable models of the given logic program.