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


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.


Mathematical Logic Modal Operator Computational Linguistic Model Property Kripke Model 
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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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