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Matematicheskie Zametki, 2014, Volume 96, Issue 4, Pages 609–622
DOI: https://doi.org/10.4213/mzm10442 (Mi mzm10442) 		 
This article is cited in 24 scientific papers (total in 24 papers)

Circular Proofs for the Gödel–Löb Provability Logic

D. S. Shamkanovab

a Steklov Mathematical Institute of the Russian Academy of Sciences
b National Research University "Higher School of Economics", Moscow
Full-text PDF (498 kB) Citations (24)
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DOI: https://doi.org/10.4213/mzm10442
Abstract: Sequent calculus for the provability logic $\mathsf{GL}$ 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 $\mathsf{GL}$.
Keywords: provability logic, sequent calculus, circular proof, the Gödel–Löb logic, the Lyndon interpolation property, split sequent.
Funding agency Grant number
Russian Foundation for Basic Research 11-01-00281-а
11-01-00947-а
12-01-00888-а
Ministry of Education and Science of the Russian Federation НШ-5593.2012.1
Received: 16.12.2013
Revised: 20.03.2014
English version:
Mathematical Notes, 2014, Volume 96, Issue 4, Pages 575–585
DOI: https://doi.org/10.1134/S0001434614090326
Bibliographic databases:
Document Type: Article
UDC: 510.6
Language: Russian
Citation: D. S. Shamkanov, “Circular Proofs for the Gödel–Löb Provability Logic”, Mat. Zametki, 96:4 (2014), 609–622; Math. Notes, 96:4 (2014), 575–585
Citation in format AMSBIB
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    • This publication is cited in the following 24 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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