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Abstract: A refutation mechanism is introduced into logic programming, dual to the usual proof mechanism; then negation is treated via refutation. A four-valued logic is appropriate for the semantics: true, false, neither, both. Inconsistent programs are allowed, but inconsistencies remain localized. The four-valued logic is a well-known one, due to Belnap, and is the simplest example of Ginsberg's bilattice notion. An e#cient implementation based on semantic tableaux is sketched; it reduces to SLD... (Update)
Context of citations to this paper: More
.... (such as annotated logic programs [40, 41] or bilattice based logics [5, 21, 33] together with non classical refutation procedures [20, 30, 40] that allow to detect inconsistent parts of a database and maintain them. A closely related topic is the problem of giving consistent...
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1.1: Bilattices and the Semantics of Logic Programming - Fitting (1989) (Correct)
0.4: Bilattices In Logic Programming - Fitting (1990) (Correct)
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0.4: Relevance Sensitive Belief Structures - Chopra, Parikh (2000) (Correct)
0.4: The Family of Stable Models - Fitting (1993) (Correct)
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16: Bilattices and the semantics of logic programming - Fitting - 1991
14: Multivalued logics: A uniform approach to reasoning in artificial intelligence (context) - Ginsberg - 1988
11: A useful four-valued logic (context) - Belnap - 1977
BibTeX entry: (Update)
M. C. Fitting. (1989) Negation as Refutation, Proc. 4th Symp. on Logic in Computer Science, Asilomar, CA, pp. 63-70. http://citeseer.ist.psu.edu/fitting89negation.html More
@inproceedings{ fitting89negation,
author = "Melvin Fitting",
title = "Negation As Refutation",
booktitle = "Logic in Computer Science",
pages = "63-70",
year = "1989",
url = "citeseer.ist.psu.edu/fitting89negation.html" }
Citations (may not include all citations):258 A lattice-theoretical fixpoint theorem and its applications (context) - Tarski - 1955
248 The Semantics of predicate logic as a programming language (context) - van Emden, Kowalski - 1976 ACM DBLP
235 First Order Logic (context) - Smullyan - 1968 ACM
186 Negation in logic programming (context) - Kunen - 1987 ACM DBLP
183 A Useful four-valued logic (context) - Belnap - 1977
144 Contributions to the theory of logic programming (context) - Apt, van Emden - 1982 ACM DBLP
120 Bilattices and the semantics of logic programming - Fitting ACM DBLP
82 Signed data dependencies in logic programs (context) - Kunen ACM DBLP
32 Multivalued Logics: A Uniform Approach to Inference in Artif.. - Ginsberg
26 Multi-valued logics (context) - Ginsberg - 1986 ACM DBLP
22 Theoretical Computer Science (context) - Fitting, models et al. - 1986 ACM
13 Kleene semantics for logic programs (context) - Fitting, Kripke - 1985
7 A Unifying principle in quantification theory (context) - Smullyan - 1963
6 Four valued semantics and the liar (context) - Visser - 1984
4 Introduction to Methmathematics (context) - Kleene - 1950
2 Springer Lecture Notes in Computer Science (context) - Blair, Subrahmanian et al.
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://math240.lehman.cuny.edu/fitting/bookspapers/logprog.html):
Bilattices and the Semantics of Logic Programming - Fitting (1989) (Correct)
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