Lithuanian Mathematical Journal

, Volume 45, Issue 1, pp 94–101 | Cite as

Path calculus in the modal logic S4

  • S. Norgėla


We describe the tableau and inverse calculi for the propositional modal logic S4. The formulas are treated as sets of paths. We obtain the upper bound for the number of applications of rules in the deduction tree.


modal logic Stableau method inverse method 


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  1. 1.
    A. Degtyarev and A. Voronkov, The inverse method, Handbook of Automated Reasoning, Elsevier Science Publishers (2001).Google Scholar
  2. 2.
    G. Mints, V. Orevkov, and T. Tammet, Transfer of sequent calculus strategies to resolution for S4, Proof Theory and Modal Logic, Kluwer Academic Publishers (1996).Google Scholar
  3. 3.
    G. Mints, Gentzen-type systems and resolution rule. Part I, Lecture Notes in Comput. Sci., 417, 198–231 (1988).Google Scholar
  4. 4.
    S. Norgėla, Decidability of some classes of modal logic (, Lith. Math. J., 42(2), 174–181 (2002).CrossRefGoogle Scholar
  5. 5.
    A. Voronkov, How to optimize proof-search in modal logics: new methods of proving redundancy criteria for sequent calculi, ACM Trans. Comput. Logic, 1(4), 182–215 (2001).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • S. Norgėla
    • 1
  1. 1.Vilnius UniversityVilniusLithuania

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