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Completeness for propositional logic programs with negation

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Methodologies for Intelligent Systems (ISMIS 1991)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 542))

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Abstract

Whether logic programming is declarative depends on the technical condition of soundness and completeness: answers produced by resolution should be exactly the logical consequences of an easily understandable completion of the program. For SLDNF-resolution (on which Prolog is based), and for programs with negation, this goal has not yet been achieved, even at the propositional level.

In this paper we prove soundness and completeness of SLDNF-resolution for the full class of propositional programs with negation (including normal programs). This is done in several ways: in classical, intuitionistic, intermediate, and modal logics. In each version we use an intuitively natural program completion, which is different from Clark's completion. The results of the paper can be of interest for rule-based expert systems which represent knowledge in propositional logic.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Miami, P.O. Box 249085, 33124, Coral Gables, Florida

    Jan A. Plaza

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  1. Jan A. Plaza
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Z. W. Ras M. Zemankova

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© 1991 Springer-Verlag Berlin Heidelberg

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Plaza, J.A. (1991). Completeness for propositional logic programs with negation. In: Ras, Z.W., Zemankova, M. (eds) Methodologies for Intelligent Systems. ISMIS 1991. Lecture Notes in Computer Science, vol 542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54563-8_123

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  • DOI: https://doi.org/10.1007/3-540-54563-8_123

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54563-7

  • Online ISBN: 978-3-540-38466-3

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