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Model Generation Theorem Proving with Finite Interval Constraints

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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

Model generation theorem proving (MGTP) is a class of deduction procedures for first-order logic that were successfully used to solve hard combinatorial problems. For some applications the representation of models in MGTP and its extension CMGTP is too redundant. Here we suggest to extend members of model candidates in such a way that a predicate p can have not only terms as arguments, but at certain places also subsets of totally ordered finite domains. The ensuing language and deduction system relies on constraints based on finite intervals in totally ordered sets and is called IV-MGTP. It is related to constraint programming and many-valued logic, but differs significantly from either. We show soundness and completeness of IV-MGTP. First results with our implementation show considerable potential of the method.

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Author information

Authors and Affiliations

  1. Department of Computing Science, Chalmers Technical University, 41296, Gothenburg, Sweden

    Reiner Hähnle

  2. Department of Intelligent Systems, Kyushu University, Kasuga Kouen 6-1, Kasuga-shi, Fukuoka, 816, Japan

    Ryuzo Hasegawa

  3. Information Technologies Development Department, Mitsubishi Research Institute, Inc., Tokyo, 100-8141, Japan

    Yasuyuki Shirai

Authors
  1. Reiner Hähnle
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  2. Ryuzo Hasegawa
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  3. Yasuyuki Shirai
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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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Hähnle, R., Hasegawa, R., Shirai, Y. (2000). Model Generation Theorem Proving with Finite Interval Constraints. 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_19

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  • DOI: https://doi.org/10.1007/3-540-44957-4_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67797-0

  • Online ISBN: 978-3-540-44957-7

  • eBook Packages: Springer Book Archive

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