The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Characterizations of the Disjunctive Well-Founded Semantics: Confluent Calculi and Iterated GCWA
Journal of Automated Reasoning
Comparisons and computation of well-founded semantics for disjunctive logic programs
ACM Transactions on Computational Logic (TOCL)
Minimum model semantics for logic programs with negation-as-failure
ACM Transactions on Computational Logic (TOCL)
Annals of Mathematics and Artificial Intelligence
A well-founded semantics with disjunction
ICLP'05 Proceedings of the 21st international conference on Logic Programming
Analysing and extending well-founded and partial stable semantics using partial equilibrium logic
ICLP'06 Proceedings of the 22nd international conference on Logic Programming
Modularity in the rule interchange format
RuleML'2011 Proceedings of the 5th international conference on Rule-based reasoning, programming, and applications
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We present a purely model-theoretic semantics for disjunctive logic programs with negation, building on the infinite-valued approach recently introduced for normal logic programs [9]. In particular, we show that every disjunctive logic program with negation has a nonempty set of minimal infinite-valued models. Moreover, we show that the infinite-valued semantics can be equivalently defined using Kripke models, allowing us to prove some properties of the new semantics more concisely. In particular, for programs without negation, the new approach collapses to the usual minimal model semantics, and when restricted to normal logic programs, it collapses to the well-founded semantics. Lastly, we show that every (propositional) program has a finite set of minimal infinite-valued models which can be identified by restricting attention to a finite subset of the truth values of the underlying logic.