Finite bases of admissible rules for the logic S52C

  • Mikhail Golovanov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1234)


We study bimodal logic system S52C having two modal operators □0 and □1, each of which satisfies the axioms of S5 and in addition, an axiom for commutability of modal operators: □01p]≡□10p. The main result of this paper establishes that the bimodal logic S52C and all its extensions have finite bases for admissible inference rules. We also show that even though the logic S52C is not locally finite, any proper extension of S52C is already locally finite. Moreover, the universal theory of the free algebra of any S52C-logic is decidable. It is shown also that any S52C-logic λ with the adjoined inference rule
is structurally complete and that logic has the same set of theorems as the logic λ.


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  1. 1.
    V.V.Rybakov, Admissible rules for logics, which are extension of S4.3, Siberian math. j., 25, N 5, (1984), 141–145.Google Scholar
  2. 2.
    Fine K. Logics Containing S4.3. Z. für Math. Logic and Grundl. Math., V.17, 1971, 371–376.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Mikhail Golovanov
    • 1
  1. 1.Mathematics DepartmentKrasnoyarsk UniversityKrasnoyarskRussia

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