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Finding Tractable Formulas in NNF

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Computational Logic — CL 2000 (CL 2000)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1861))

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Abstract

Many applications in Computer Science require to represent knowledge and to reason with non normal form formulas. However, most of the advances in tractable reasoning are applied only to CNF formulas. In this paper, we extend tractability to several classes of non normal formulas which are of high practical interest. Thus, we first define three non normal Horn-like classes of formulas F 1 ∧F 2 ∧... ∧F n where each F i is constituted by a disjunction of two optional terms F i = NNF i - ∨ C i +: the first one is in Negation Normal Form (NNF) composed exclusively with negative literals and the second one is a conjunction of positive propositions. These formulas codify the same problems that the Horn formulas but with significantly, even exponentially, less propositional symbols. Second, we define sound and refutational complete inference rule sets for each class. Our third contribution consists in the design of a sound, complete and strictly linear running time algorithm for each class. As a result, the time required by our linear algorithms running on the defined non normal Horn-like formulas can be exponentially less than that required by the existing linear Horn-SAT algorithms.

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Author information

Authors and Affiliations

  1. Artificial Intelligence Research Institute (IIIA), Spanish Scientific Research Council (CSIC), Campus UAB, s/n, 08193, Bellaterra, Barcelona, Spain

    Edgar Altamirano & Gonçal Escalada-Imaz

Authors
  1. Edgar Altamirano
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  2. Gonçal Escalada-Imaz
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Editor information

Editors and Affiliations

  1. The Australian National University, Australia

    John Lloyd

  2. Simon Fraser University, Canada

    Veronica Dahl

  3. Universität Koblenz, Germany

    Ulrich Furbach

  4. The University of Birmingham, UK

    Manfred Kerber

  5. University of Manchester, UK

    Kung-Kiu Lau

  6. The Pennsylvania State University, USA

    Catuscia Palamidessi

  7. Universidade Nova de Lisboa, Portugal

    Luís Moniz Pereira

  8. The Hebrew University of Jerusalem, Israel

    Yehoshua Sagiv

  9. The University of Melbourne, Australia

    Peter J. Stuckey

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© 2000 Springer-Verlag Berlin Heidelberg

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Altamirano, E., Escalada-Imaz, G. (2000). Finding Tractable Formulas in NNF. In: Lloyd, J., et al. Computational Logic — CL 2000. CL 2000. Lecture Notes in Computer Science(), vol 1861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44957-4_33

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  • DOI: https://doi.org/10.1007/3-540-44957-4_33

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67797-0

  • Online ISBN: 978-3-540-44957-7

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