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Abstract: We prove the completeness of extended SLDNF-resolution for the new class of "-programs with respect to the three-valued completion of a logic program. Not only the class of allowed programs but also the class of definite programs are contained in the class of "-programs. To understand better the three-valued completion of a logic program we introduce a formal system for three-valued logic in which one can derive exactly the three-valued consequences of the completion of a logic program. The... (Update)
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...is the empty set and J P n 1 is the structure #P (J P n ) The following theorem is a variant of Theorem 6. 3 in [12] or Corollary 32 in [18]. Theorem 5.1 Let P be a program and #[#x ] be a positive L formula. If #comp(P ) # #[#x ] then there exists a natural number n such that...
.... deductive systems introduced by Halln as and Schroeder Heister [HSH90, SH91] and also adopted by J ager and St ark 10 [J ag94, JS98, St a91, St a94] for the analysis of logic programming starts with a proof theoretic perspective, too. Mainly, it emphasizes the usefulness and...
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BibTeX entry: (Update)
Robert Stark. A complete axiomatization of the three-valued completion of logic programs. Journal of Logic and Computation, 1(6):811--834, 1991. http://citeseer.ist.psu.edu/stark91complete.html More
@article{ stark91complete,
author = "Robert F. Stark",
title = "A Complete Axiomatization of the Three-Valued Completion of Logic Programs",
journal = "Journal of Logic and Computation",
volume = "1",
number = "6",
pages = "811-834",
year = "1991",
url = "citeseer.ist.psu.edu/stark91complete.html" }
Citations (may not include all citations):1838 Foundations of Logic Programming (context) - Lloyd - 1987
759 Negation as failure (context) - Clark - 1978
435 Towards a theory of declarative knowledge (context) - Apt, Blair et al. - 1987
186 Negation in logic programming (context) - Kunen - 1987
174 A Kripke-Kleene semantics for logic programs (context) - Fitting - 1985
82 Signed data dependencies in logic programs (context) - Kunen - 1989
67 Negation as failure using tight derivations for general logi.. (context) - Van Gelder - 1987
29 A completeness theorem for SLDNF-resolution (context) - Cavedon, Lloyd - 1989
22 Negation as failure: A comparison of Clark's completed data .. (context) - Shepherdson - 1984
22 Completeness of the negation as failure rule (context) - Jaffar, Lassez et al. - 1983
19 Proof Theory (context) - Schutte - 1977
15 A sound and complete semantics for a version of negation as .. (context) - Shepherdson - 1989
14 IC-PROLOG language features (context) - Clark, McCabe et al. - 1982
12 A direct proof for the completeness of SLD-resolution (context) - Stark - 1990
10 Negation as failure II (context) - Shepherdson - 1985
8 Proof Theory and Logical Complexitiy (context) - Girard - 1987
The graph only includes citing articles where the year of publication is known.
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