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On Provability Logics with Linearly Ordered Modalities

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Abstract

We introduce the logics GLP Λ, a generalization of Japaridze’s polymodal provability logic GLP ω where Λ is any linearly ordered set representing a hierarchy of provability operators of increasing strength. We shall provide a reduction of these logics to GLP ω yielding among other things a finitary proof of the normal form theorem for the variable-free fragment of GLP Λ and the decidability of GLP Λ for recursive orderings Λ. Further, we give a restricted axiomatization of the variable-free fragment of GLP Λ.

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Authors and Affiliations

  1. V. A. Steklov Mathematical Institute, RAS, Moscow M.V. Lomonosov State University, National Research University Higher School of Economics, Moscow, Russia

    Lev D. Beklemishev

  2. Department of Computer Science and Artificial Intelligence, Universidad de Sevilla, Seville, Spain

    David Fernández-Duque

  3. Department of Logic, History and Philosophy of Science, Universitat de Barcelona, Barcelona, Spain

    Joost J. Joosten

Authors
  1. Lev D. Beklemishev
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  2. David Fernández-Duque
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  3. Joost J. Joosten
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Correspondence to David Fernández-Duque.

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Beklemishev, L.D., Fernández-Duque, D. & Joosten, J.J. On Provability Logics with Linearly Ordered Modalities. Stud Logica 102, 541–566 (2014). https://doi.org/10.1007/s11225-013-9490-7

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