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Stable semantics for disjunctive programs

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Abstract

We 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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Authors and Affiliations

  1. Department of Computer Science, The University of California at Riverside, 92521-0304, Riverside, CA, USA

    Teodor C. Przymusinski

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  1. Teodor C. Przymusinski
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Additional information

Partially supported by the National Science Foundation grant #IRI-89-10729, the Army Research Office grant #27079-ML-SAH and the Swedish National Board for Technical Development grant #90-1676. This paper was completed while the author was visiting the Computer Science Department at the University of Linkoping in Sweden.

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Przymusinski, T.C. Stable semantics for disjunctive programs. New Gener Comput 9, 401–424 (1991). https://doi.org/10.1007/BF03037171

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