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Many−Valued Disjunctive Logic Programs with Probabilistic Semantics

Thomas Lukasiewicz

Abstract

We present many-valued disjunctive logic programs in which classical disjunctive logic program clauses are extended by a truth value that respects the material implication. Interestingly, these many-valued disjunctive logic programs have both a probabilistic semantics in probabilities over possible worlds and a truth-functional semantics. We then define minimal, perfect, and stable models and show that they have the same properties like their classical counterparts. In particular, perfect and stable models are always minimal models. Under local stratification, the perfect model semantics coincides with the stable model semantics. Finally, we show that some special cases of propositional many-valued disjunctive logic programming under minimal, perfect, and stable model semantics have the same complexity like their classical counterparts.

Book Title
Proceedings of the 5th International Conference on Logic Programming and Nonmonotonic Reasoning‚ LPNMR 1999‚ El Paso‚ Texas‚ USA‚ December 2−4‚ 1999
Editor
Michael Gelfond and Nicola Leone and Gerald Pfeifer
ISBN
3−540−66749−0
Pages
277−289
Publisher
Springer
Series
Lecture Notes in Computer Science
Volume
1730
Year
1999