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 $$ \hat P $$ the disjunctive (respectively, partial disjunctive) stable semantics ofP coincides with the autoepistemic (respectively, 3-valued autoepistemic) semantics of $$ \hat P $$ .

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