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Mathematical Notes

, Volume 96, Issue 3–4, pp 575–585 | Cite as

Circular proofs for the Gödel-Löb provability logic

  • D. S. Shamkanov
Article

Abstract

Sequent calculus for the provability logic GL is considered, in which provability is based on the notion of a circular proof. Unlike ordinary derivations, circular proofs are represented by graphs allowed to contain cycles, rather than by finite trees. Using this notion, we obtain a syntactic proof of the Lyndon interpolation property for GL.

Keywords

provability logic sequent calculus circular proof the Gödel-Löb logic the Lyndon interpolation property split sequent 

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Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia
  2. 2.National Research University Higher School of EconomicsMoscowRussia

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