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Mat. Zametki, 2014, Volume 96, Issue 4, Pages 609–622 (Mi mz10442)  

This article is cited in 10 scientific papers (total in 10 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

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


DOI: https://doi.org/10.4213/mzm10442

Full text: PDF file (498 kB)
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English version:
Mathematical Notes, 2014, 96:4, 575–585

Bibliographic databases:

UDC: 510.6
Received: 16.12.2013
Revised: 20.03.2014

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. S. Shamkanov, “A realization theorem for the Gödel-Löb provability logic”, Sb. Math., 207:9 (2016), 1344–1360  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. S. L. Kuznetsov, “On translating Lambek grammars with one division into context-free grammars”, Proc. Steklov Inst. Math., 294 (2016), 129–138  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. B. Afshari, G. E. Leigh, “Cut-free completeness for modal $\mu$-calculus”, 2017 32nd Annual Acm/IEEE Symposium on Logic in Computer Science (LICS), IEEE Symposium on Logic in Computer Science, IEEE, 2017  mathscinet  isi
    4. S. Kuznetsov, “The Lambek calculus with iteration: two variants”, Logic, Language, Information, and Computation, WoLLIC 2017 (London, UK, July 18–21, 2017), Lecture Notes in Computer Science, 10388, eds. J. Kennedy, R. DeQueiroz, Springer International Publishing Ag, 2017, 182–198  crossref  mathscinet  zmath  isi  scopus
    5. Yu. Savateev, D. Shamkanov, “Cut-elimination for the modal Grzegorczyk logic via non-well-founded proofs”, Logic, Language, Information, and Computation, WoLLIC 2017 (London, UK, July 18–21, 2017), Lecture Notes in Computer Science, 10388, eds. J. Kennedy, R. DeQueiroz, Springer International Publishing Ag, 2017, 321–335  crossref  mathscinet  zmath  isi  scopus
    6. D. Shamkanov, “Global neighbourhood completeness of the Gödel-Lob provability logic”, Logic, Language, Information, and Computation, WoLLIC 2017 (London, UK, July 18–21, 2017), Lecture Notes in Computer Science, 10388, eds. J. Kennedy, R. DeQueiroz, Springer International Publishing Ag, 2017, 358–370  crossref  mathscinet  zmath  isi  scopus
    7. R. Kuznets, “Multicomponent proof-theoretic method for proving interpolation properties”, Ann. Pure Appl. Log., 169:12, SI (2018), 1369–1418  crossref  mathscinet  zmath  isi  scopus
    8. K. A. Jobczyk, A. Ligeza, “An epistemic Halpern-Shoham logic for gradable justification”, 2018 IEEE International Conference on Fuzzy Systems (Fuzz-IEEE), IEEE International Conference on Fuzzy Systems, IEEE, 2018  isi
    9. Kavvos G.A., “Dual-Context Calculi For Modal Logic”, Log. Meth. Comput. Sci., 16:3 (2020), 10  crossref  mathscinet  isi
    10. Shamkanov D., “Non-Well-Founded Derivations in the Godel-Lob Provability Logic”, Rev. Symb. Log., 13:4 (2020), PII S1755020319000613, 776–796  crossref  mathscinet  isi
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