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Studia Logica

, Volume 39, Issue 4, pp 325–333 | Cite as

On the size of refutation Kripke models for some linear modal and tense logics

  • Hiroakira Ono
  • Akira Nakamura
Article

Abstract

LetL be any modal or tense logic with the finite model property. For eachm, definer L (m) to be the smallest numberr such that for any formulaA withm modal operators,A is provable inL if and only ifA is valid in everyL-model with at mostr worlds. Thus, the functionr L determines the size of refutation Kripke models forL. In this paper, we will give an estimation ofr L (m) for some linear modal and tense logicsL.

Keywords

Mathematical Logic Modal Operator Computational Linguistic Model Property Kripke Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    S.A. Cook,The complexity of theorem proving procedures, Proceedings of Third Annual ACM Symposium on Theory of Computing (1971) 151–158.Google Scholar
  2. [2]
    R.E. Ladner,The computational complexity of provability in systems of modal prepositional logic, SIAM J. on Computing, 6 (1977) 467–480.Google Scholar
  3. [3]
    R.P. McArthur,Tense logic D. Reidel, 1976.Google Scholar
  4. [4]
    H. Ono andA. Nakamura,The computational complexity of satisfiability of modal propositional logic S4.3. Tech. Rep. No.C-5, Dept. of Applied Math., Hiroshima Univ. (1979).Google Scholar
  5. [5]
    H. Rasiowa andR. Sikorski,The mathematics of metamathematics,Monografie Matematyczne 41, PWN, 1963.Google Scholar
  6. [6]
    K. Segerberg,An essay in classical modal logic,Filosofiska Studier 13, Uppsala Univ. (1971).Google Scholar

Copyright information

© Polish Academy of Sciences 1980

Authors and Affiliations

  • Hiroakira Ono
    • 1
    • 2
  • Akira Nakamura
    • 1
    • 2
  1. 1.Faculty of Integrated arts and SciencesHiroshima UniversityHiroshimaJapan
  2. 2.Department of Applied MathematicsHiroshima UniversityHiroshimaJapan

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