Journal of Logic Programming
Foundations of logic programming; (2nd extended ed.)
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Well-founded semantics coincides with three-valued stable semantics
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Journal of Logic Programming
The alternating fixpoint of logic programs with negation
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Temporal and modal logic programming: an annotated bibliography
ACM SIGART Bulletin
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Journal of the ACM (JACM)
ACM Transactions on Programming Languages and Systems (TOPLAS)
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Strong equivalence of logic programs under the infinite-valued semantics
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Well-founded semantics for Boolean grammars
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A purely model-theoretic semantics for disjunctive logic programs with negation
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
A game-theoretic characterization of Boolean grammars
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A sufficient condition for strong equivalence under the well-founded semantics
ICLP'05 Proceedings of the 21st international conference on Logic Programming
Well-Founded semantics for boolean grammars
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
Preferential Regular Path Queries
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Extensional Higher-Order Logic Programming
ACM Transactions on Computational Logic (TOCL)
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We give a purely model-theoretic characterization of the semantics of logic programs with negation-as-failure allowed in clause bodies. In our semantics, the meaning of a program is, as in the classical case, the unique minimum model in a program-independent ordering. We use an expanded truth domain that has an uncountable linearly ordered set of truth values between False (the minimum element) and True (the maximum), with a Zero element in the middle. The truth values below Zero are ordered like the countable ordinals. The values above Zero have exactly the reverse order. Negation is interpreted as reflection about Zero followed by a step towards Zero; the only truth value that remains unaffected by negation is Zero. We show that every program has a unique minimum model MP, and that this model can be constructed with a TP iteration which proceeds through the countable ordinals. Furthermore, we demonstrate that MP can alternatively be obtained through a construction that generalizes the well-known model intersection theorem for classical logic programming. Finally, we show that by collapsing the true and false values of the infinite-valued model MP to (the classical) True and False, we obtain a three-valued model identical to the well-founded one.