The Well Founded Semantics for Disjunctive Logic Programs

We extend the well-founded semantics of Van Gelder, Ross and Schlipf to disjunctive logic programs. We propose a “strong” semantics, in which disjunction is treated exclusively, and a “weak” semantics in which disjunction is treated inclusively. The strong semantics infers a subset of the information inferred under the perfect model approach of Przymusinski for locally stratified programs, but is well defined for all programs. The weak semantics generalizes the disjunctive database rule of Ross and Topor. We then define an “optimal” semantics which treats each rule either inclusively or exclusively according to the programmer's specification. We compare our proposed semantics to previous approaches, and examine some of its properties.

[1]  Melvin Fitting,et al.  A Kripke-Kleene Semantics for Logic Programs , 1985, J. Log. Program..

[2]  Kenneth Kunen,et al.  Negation in Logic Programming , 1987, J. Log. Program..

[3]  Teodor C. Przymusinski,et al.  The extended closed world assumption and its relationship to parallel circumscription , 1985, PODS '86.

[4]  David Harel,et al.  Horn Clauses Queries and Generalizations , 1985, J. Log. Program..

[5]  John C. Shepherdson,et al.  Negation in Logic Programming , 1988, Foundations of Deductive Databases and Logic Programming..

[6]  Adrian Walker,et al.  Towards a Theory of Declarative Knowledge , 1988, Foundations of Deductive Databases and Logic Programming..

[7]  Jörg H. Siekmann,et al.  Universal Unification , 1982, GWAI.

[8]  Kenneth A. Ross,et al.  A procedural semantics for well founded negation in logic programs , 1989, J. Log. Program..

[9]  Teodor C. Przymusinski.  Every logic program has a natural stratification and an iterated least fixed point model , 1989, PODS.

[10]  John C. Shepherdson,et al.  Negation as Failure II , 1985, J. Log. Program..

[11]  Allen Van Gelder,et al.  Negation as Failure using Tight Derivations for General Logic Programs , 1988, J. Log. Program..

[12]  Teodor C. Przymusinski.  On the Declarative Semantics of Deductive Databases and Logic Programs , 1988, Foundations of Deductive Databases and Logic Programming..

[13]  Kenneth A. Ross,et al.  Unfounded sets and well-founded semantics for general logic programs , 1988, PODS.

[14]  Jack Minker,et al.  On Indefinite Databases and the Closed World Assumption , 1987, CADE.

[15]  Keith L. Clark,et al.  Negation as Failure , 1987, Logic and Data Bases.