The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Well founded semantics for logic programs with explicit negation
ECAI '92 Proceedings of the 10th European conference on Artificial intelligence
The Semantics of Predicate Logic as a Programming Language
Journal of the ACM (JACM)
Strongly equivalent logic programs
ACM Transactions on Computational Logic (TOCL) - Special issue devoted to Robert A. Kowalski
Characterizations of the Disjunctive Well-Founded Semantics: Confluent Calculi and Iterated GCWA
Journal of Automated Reasoning
A New Logical Characterisation of Stable Models and Answer Sets
NMELP '96 Selected papers from the Non-Monotonic Extensions of Logic Programming
Annals of Mathematics and Artificial Intelligence
Semantical characterizations and complexity of equivalences in answer set programming
ACM Transactions on Computational Logic (TOCL)
Annals of Mathematics and Artificial Intelligence
Strong negation in well-founded and partial stable semantics for logic programs
IBERAMIA-SBIA'06 Proceedings of the 2nd international joint conference, and Proceedings of the 10th Ibero-American Conference on AI 18th Brazilian conference on Advances in Artificial Intelligence
Analysing and extending well-founded and partial stable semantics using partial equilibrium logic
ICLP'06 Proceedings of the 22nd international conference on Logic Programming
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This paper is devoted to logical aspects of two closely related semantics for logic programs: the partial stable model semantics of Przymusinski [20] and the well-founded semantics of Van Gelder, Ross and Schlipf [24]. For many years the following problem remained open: Which (non-modal) logic can be regarded as yielding an adequate foundation for these semantics in the sense that its minimal models (appropriately defined) coincide with the partial stable models of a logic program? Initial work on this problem was undertaken by Cabalar [5] who proposed a frame-based semantics for a suitable logic which he called HT 2. Preliminary axiomatics of HT 2 was presented in [6]. In this paper we analyse HT 2 frames and identify them as structures of a logic N * having intuitionistic positive connectives and Routley negation and give a natural axiomatics for HT 2. We define a notion of minimal, total HT 2 model which we call partial equilibrium model . We show that for logic programs these models coincide with partial stable models, and we propose the resulting partial equilibrium logic as a logical foundation for partial stable and well-founded semantics. Finally, we discuss the strong equivalence for theories and programs in partial equilibrium logic.