Teodor C. Przymusinski

Stable semantics for disjunctive programs

AbstractWe introduce the stable model semantics fordisjunctive logic programs and deductive databases, which generalizes the stable model semantics, defined earlier for normal (i.e., non-disjunctive) programs. Depending on whether only total (2-valued) or all partial (3-valued) models are used we obtain thedisjunctive stable semantics or thepartial disjunctive stable semantics, respectively. The proposed semantics are shown to have the following properties:• For normal programs, the disjunctive (respectively, partial disjunctive) stable semantics coincides with thestable (respectively,partial stable) semantics.• For normal programs, the partial disjunctive stable semantics also coincides with thewell-founded semantics.• For locally stratified disjunctive programs both (total and partial) disjunctive stable semantics coincide with theperfect model semantics.• The partial disjunctive stable semantics can be generalized to the class ofall disjunctive logic programs.• Both (total and partial) disjunctive stable semantics can be naturally extended to a broader class of disjunctive programs that permit the use ofclassical negation.• After translation of the programP into a suitable autoepistemic theory

On the relationship between circumscription and negation as failure

\hat P

Every logic program has a natural stratification and an iterated least fixed point model

the disjunctive (respectively, partial disjunctive) stable semantics ofP coincides with the autoepistemic (respectively, 3-valued autoepistemic) semantics of

Static semantics for normal and disjunctive logic programs

\hat P

Three-valued nonmonotonic formalisms and semantics of logic programs

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The extended closed world assumption and its relationship to parallel circumscription

In this paper we investigate updates of knowledge bases represented by logic programs. In order to represent negative information, we use generalized logic programs which allow default negation not only in rule bodies but also in their heads. We start by introducing the notion of an update P U of one logic program P by another logic program U. Subsequently, we provide a precise semantic characterization of P U , and study some basic properties of program updates. In particular, we show that our update programs generalize the notion of interpretation update. We then extend this notion to compositional sequences of logic programs updates P1 P2 ; defining a dynamic program update, and thereby introducing the paradigm of dynamic logic programming. This paradigm significantly facilitates modularization of logic programming, and thus modularization of non-monotonic reasoning as a whole. Specifically, suppose that we are given a set of logic program modules, each describing a diAerent state of our knowledge of the world. DiAerent states may represent diAerent time points or diAerent sets of priorities or perhaps even diAerent viewpoints. Consequently, program modules may contain mutually contradictory as well as overlapping information. The role of the dynamic program update is to employ the mutual relationships existing between diAerent modules to precisely determine, at any given module composition stage, the declarative as well as the procedural semantics of the combined program resulting from the modules. ” 2000 Elsevier Science Inc. All rights reserved.