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Siberian Mathematical Journal

, Volume 56, Issue 3, pp 565–568 | Cite as

On the linear logic of knowledge and time with intransitive time relation

  • V. F. YunEmail author
Article

Abstract

In [1], there was introduced a linear multi-modal logic of knowledge and time with intransitive time relation as the set of formulas valid in frames of special kind. The article [2] proposed some calculus \(AS_{LTK_r }\) that is connected with the class of these frames. In the present article we find a formula of the linear logic of knowledge and time which is underivable in \(AS_{LTK_r }\).

Keywords

multi-modal logic Kripke frame axiomatization completeness 

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References

  1. 1.
    Lukyanchuk A., “Decidability of multi-modal logic LTK of linear time and knowledge,” J. Siberian Federal Univ., 6, No. 2, 220–226 (2013).Google Scholar
  2. 2.
    Luk’yanchuk A. N. and Rimatskiĭ V. V., “An axiomatization for the linear logic of knowledge and time LTK r with intransitive time relation,” Siberian Math. J., 54, No. 6, 1037–1045 (2013).zbMATHCrossRefGoogle Scholar
  3. 3.
    Chagrov A. and Zakharyaschev M., Modal Logic, Oxford Univ. Press, Oxford (1997) (Oxford Logic Guides; Book 35).zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirsk State UniversityNovosibirskRussia

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