Properties of substitutions and unifications
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A sound and complete semantics for a version of negation as failure
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Every logic program has a natural stratification and an iterated least fixed point model
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Well-founded semantics coincides with three-valued stable semantics
Fundamenta Informaticae
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
On the relations between stable and well-founded semantics of logic programs
Theoretical Computer Science - Selected papers of the Second International Conference on algebraic and logic programming, Nancy, France, October 1–3, 1990
A procedural semantics for well-founded negation in logic programs
Journal of Logic Programming
Preferred extensions are partial stable models
Journal of Logic Programming
The alternating fixpoint of logic programs with negation
PODS '89 Selected papers of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Query evaluation in deductive databases with alternating fixpoint semantics
ACM Transactions on Database Systems (TODS)
Tabled evaluation with delaying for general logic programs
Journal of the ACM (JACM)
SLDNF resolution with non-safe rule and fixpoint semantics for general logic programs
Theoretical Computer Science
A non-ground realization of the stable and well-founded semantics
Theoretical Computer Science
Soundness of abductive proof procedure with respect to constraint for non-ground abducibles
Theoretical Computer Science
Foundations of Logic Programming
Foundations of Logic Programming
An automated reasoning for diagnostic knowledge in a distributed environment
ISICT '03 Proceedings of the 1st international symposium on Information and communication technologies
Logic programming with default, weak and strict negations
Theory and Practice of Logic Programming
A calculus effectively performing event formation with visualization
ISHPC'05/ALPS'06 Proceedings of the 6th international symposium on high-performance computing and 1st international conference on Advanced low power systems
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This paper presents a sound and complete procedure with respect to the 3-valued stable model semantics. The procedure is regarded as an extension of Eshghi and Kowalski abductive proof procedure, involving finite or countably infinite SLD resolution, as well as finite or countably infinite negative recursion caused by negation as failure. The procedure makes use of the set of negative literals (the set of abducibles) for the negation as failure to be implemented. The set of abducibles is not only applicable to the extraction of explanations for abduction as in Kakas et al. (J. Logic Comput. 2 (1992) 719-770) but also specified for what stable model is now computed in the procedure, because a 3-valued stable model is not always the least (that is, the well-founded model). The procedure also contains nondeterminism in the choices of what ground negative literals are used for negation as failure. By the assumptions of some adequate choices, the procedure is well-defined inductively. Copyright 2001 Elsevier Science B.V.