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Static semantics for normal and disjunctive logic programs

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Abstract

In this paper, we propose a newsemantic framework for disjunctive logic programming by introducingstatic expansions of disjunctive programs. The class of static expansions extends both the classes of stable, well-founded and stationary models of normal programs and the class of minimal models of positive disjunctive programs. Any static expansion of a programP provides the corresponding semantics forP consisting of the set of all sentences logically implied by the expansion. We show that among all static expansions of a disjunctive programP there is always theleast static expansion, which we call thestatic completion ¯P ofP. The static completion¯P can be defined as the least fixed point of a naturalminimal model operator and can be constructed by means of a simpleiterative procedure. The semantics defined by the static completion¯P is called thestatic semantics ofP. It coincides with the set of sentences that are true inall static expansions ofP. For normal programs, it coincides with the well-founded semantics. The class of static expansions represents a semantic framework which differs significantly from the other semantics proposed recently for disjunctive programs and databases. It is also defined for a much broader class of programs.

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Authors and Affiliations

  1. Department of Computer Science, University of California, 92521, Riverside, CA, USA

    Teodor C. Przymusinski

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  1. Teodor C. Przymusinski
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Dedicated to Jack Minker

Partially supported by the National Science Foundation grant # IRI-9313061.

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Przymusinski, T.C. Static semantics for normal and disjunctive logic programs. Ann Math Artif Intell 14, 323–357 (1995). https://doi.org/10.1007/BF01530826

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