Modal logics preserving admissible for S4 inference rules

  • Vladimir V. Rybakov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 933)


The aim of the current paper is to provide a complete semantics description for modal logics with finite model property which preserve all admissible in S4 inference rules, with the intention of meeting some of the needs of computer science. It is shown a modal logic λ with fmp above S4 preserves all admissible for S4 inference rules iff λ has so-called co-cover property. In turned out there are continuously many logics of this kind. Using mentioned above semantics criterion we give some precise description of all tabular logics preserving admissible for S4 rules.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    van Benthem J. A Manual of Intensional Logic. Lecture Notes, CSLI, Stanford, 1988, 135pp.Google Scholar
  2. [2]
    Clarke E.M., Grumberg O., Kurshan B.P. A Synthesis of Two Approaches for Verifying Finite State Concurrent Systems. Lecture Notes in Computer Science, No. 363, 1989, Logic at Botik'89, Springer-Verlag, 81–90.Google Scholar
  3. [3]
    Fagin R., Halpern J.Y., Vardi M.Y., What is an Inference Rule. J. of Symbolic Logic, 57(1992), No 3, 1018–1045.Google Scholar
  4. [4]
    Goldblatt R.I. Metamathematics of Modal Logics, Reports on Mathematical Logic, Vol. 6(1976), 41–78 (Part 1), 7(1976), 21–52 (Part 2).Google Scholar
  5. [5]
    Konolige K., On the Relation between Default and Autoepistemic Logic. Artificial Intelligence, V. 35 (1988), 343–382.CrossRefGoogle Scholar
  6. [6]
    Larsen K.G., Thomsen B. A Modal Process Logic, in Proceedings of Third Annual Symposium on Logic in Computer Science, Edinburgh, 1988.Google Scholar
  7. [7]
    Moore R.G., Semantical Consideration on Non-monotonic Logic. Artificial Intelligence, V.25(1985), 75–94.CrossRefGoogle Scholar
  8. [8]
    Rautenberg W. Klassische und nichtklassische Aussagenlogik, Braunschweig/Wiesbaden, 1979.Google Scholar
  9. [9]
    Rybakov V.V. Problems of Admissibility and Substitution, Logical Equations and Restricted Theories of Free Algebras. Proced. of the 8-th International. Congress of Logic Method. and Phil. of Science. Elsevier Sci. Publ., North. Holland, Amsterdam, 1989, 121–139.Google Scholar
  10. [10]
    Rybakov V.V. Problems of Substitution and Admissibility in the Modal System Grz and Intuitionistic Calculus. Annals of Pure and Applied logic V.50, 1990, 71–106.CrossRefGoogle Scholar
  11. [11]
    Rybakov V.V. Intermediate Logics Preserving Admissible Inference Rules of Heyting Calculus. Math. Logic Quart. V. 39 (1993), 403–415.Google Scholar
  12. [12]
    Shvarts G.F. Gentzen Style Systems for K45 and K45D. Lecture Notes in Computer Science, No. 363, 1989, Logic at Botik'89, Springer-Verlag, 245–255.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Vladimir V. Rybakov
    • 1
  1. 1.Mathematics DepartmentKrasnoyarsk State UniversityKrasnoyarskRussia

Personalised recommendations