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Preserving of admissible inference rules in modal logic

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Logical Foundations of Computer Science (LFCS 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 813))

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Abstract

The main result of this paper is a complete semantics description of all modal logics with finite model property that preserves all admissible for S4 inference rules: a modal logic λ with fmp above S4 preserves the admissibility iff λ has so-called co-cover property. As an application it is shown that there are continuously many logics of this kind. On base mentioned above semantical criterion, as corollary, we give some precise description of all tabular logics that preserves admissible for S4 rules.

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Authors and Affiliations

  1. Mathematics Department, Krasnoyarsk State University, av. Svobodnyi 79, 660062, Krasnoyarsk, Russia

    Vladimir V. Rybakov

Authors
  1. Vladimir V. Rybakov
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Anil Nerode Yu. V. Matiyasevich

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© 1994 Springer-Verlag Berlin Heidelberg

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Rybakov, V.V. (1994). Preserving of admissible inference rules in modal logic. In: Nerode, A., Matiyasevich, Y.V. (eds) Logical Foundations of Computer Science. LFCS 1994. Lecture Notes in Computer Science, vol 813. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58140-5_29

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  • DOI: https://doi.org/10.1007/3-540-58140-5_29

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58140-6

  • Online ISBN: 978-3-540-48442-4

  • eBook Packages: Springer Book Archive

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