Model Generation Theorem Proving with Finite Interval Constraints

  • Reiner Hähnle
  • Ryuzo Hasegawa
  • Yasuyuki Shirai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1861)


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.


Logic Program Model Candidate Conjunctive Normal Form Constraint Variable Ground Atom 
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  1. 1.
    S. Abdennadher and H. Schütz. CHRV: A flexible query language. In T. Andreasen, H. Christansen, and H. L. Larsen, eds., Proc. Int. Conf. on Flexible Query Answering Systems FQAS, Roskilde, Denmark, vol. 1495 of LNCS, pp. 1–15. Springer-Verlag, 1998.CrossRefGoogle Scholar
  2. 2.
    P. Baumgartner, U. Furbach, and I. Niemelä. Hyper tableaux. In J. J. Alferes, L. M. Pereira, and E. Orlowska, eds., Proc. European Workshop: Logics in Artificial Intelligence, vol. 1126 of LNCS, pp. 1–17. Springer-Verlag, 1996.Google Scholar
  3. 3.
    F. Benhamou. Interval constraint logic programming. In A. Podelski, editor, Constraint programming: basics and trends, Chatillon Spring School, Chatillonsur-Seine, France, 1994, vol. 910 of LNCS, pp. 1–21. Springer-Verlag, 1995.Google Scholar
  4. 4.
    H. Fujita and R. Hasegawa. A model generation theorem prover in KL1 using a ramified-stack algorithm. In K. Furukawa, editor, Proc. 8th Int. Conf. on Logic Programming, Paris/France, pp. 535–548. MIT Press, 1991.Google Scholar
  5. 5.
    R. Hähnle. Automated Deduction in Multiple-Valued Logics. OUP, 1994.Google Scholar
  6. 6.
    R. Hähnle. Tableaux and related methods. In A. Robinson and A. Voronkov, eds., Handbook of Automated Reasoning. Elsevier Science Publishers, to appear, 2000.Google Scholar
  7. 7.
    R. Hähnle, R. Hasegawa, and Y. Shirai. Model generation theorem proving with interval constraints. In F. Benhamou, W. J. Older, M. van Emden, and P. van Hentenryck, eds., Proc. of ILPS Post-Conf. Workshop on Interval Constraints, Portland/OR, USA, Dec. 1995.Google Scholar
  8. 8.
    R. Hasegawa and H. Fujita. A new implementation technique for a Model-Generation Theorem Prover to solve constraint satisfaction problems. Research Reports on Inf. Sci. and El. Eng. Vol. 4, No. 1, pp. 57–62, Kyushu Univ., 1999.Google Scholar
  9. 9.
    R. Hasegawa, H. Fujita, and M. Koshimura. MGTP: a model generation theorem prover—its advanced features and applications. In D. Galmiche, editor, Proc. Int. Conf. on Automated Reasoning with Analytic Tableaux and Related Methods, Ponta-Mousson, France, vol. 1227 of LNCS, pp. 1–15. Springer-Verlag, 1997.CrossRefGoogle Scholar
  10. 10.
    M. Kifer and E. L. Lozinskii. A logic for reasoning with inconsistency. Journal of Automated Reasoning, 9(2):179–215, Oct. 1992.Google Scholar
  11. 11.
    M. Kifer and V. S. Subrahmanian. Theory of generalized annotated logic programming and its applications. Journal of Logic Programming, 12:335–367, 1992.CrossRefMathSciNetGoogle Scholar
  12. 12.
    J. J. Lu. Logic programming with signs and annotations. Journal of Logic and Computation, 6(6):755–778, 1996.zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    U. Montanari and F. Rossi. Finite Domain Constraint Solving and Constraint Logic Programming. In F. Benhamou and A. Colmerauer, eds., Constraint Logic Programming: Selected Research, pp. 201–221. The MIT press, 1993.Google Scholar
  14. 14.
    Y. Shirai and R. Hasegawa. Two approaches for finite-domain constraint satisfaction problem: CP and MGTP. In L. Stirling, editor, Proc. 12th Int. Conf. on Logic Programming, pp. 249–263. MIT Press, 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Reiner Hähnle
    • 1
  • Ryuzo Hasegawa
    • 2
  • Yasuyuki Shirai
    • 3
  1. 1.Department of Computing ScienceChalmers Technical UniversityGothenburgSweden
  2. 2.Department of Intelligent SystemsKyushu UniversityFukuokaJapan
  3. 3.Information Technologies Development DepartmentMitsubishi Research Institute, Inc.TokyoJapan

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