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Studia Logica

, Volume 102, Issue 3, pp 541–566 | Cite as

On Provability Logics with Linearly Ordered Modalities

  • Lev D. Beklemishev
  • David Fernández-Duque
  • Joost J. Joosten
Article

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.

Keywords

Provability logic Modal logic 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Lev D. Beklemishev
    • 1
  • David Fernández-Duque
    • 2
  • Joost J. Joosten
    • 3
  1. 1.V. A. Steklov Mathematical Institute, RASMoscow M.V. Lomonosov State University, National Research University Higher School of EconomicsMoscowRussia
  2. 2.Department of Computer Science and Artificial IntelligenceUniversidad de SevillaSevilleSpain
  3. 3.Department of Logic, History and Philosophy of ScienceUniversitat de BarcelonaBarcelonaSpain

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