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May 22, 2026
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Циклические выводы в логике доказуемости Гёделя-Лёба

С. 56–58.
Shamkanov D. S.

A Hilbert-style proof system for the Godel-Lob provability logic GL is
considered, in which provability is based on the notion of a cyclic (circu-
lar) proof. Unlike ordinary derivations, these proofs can be represented
by graphs allowed to contain cycles, rather than by finite trees.

Language: Russian
Keywords: логика доказуемостициклические выводы

In book

Десятые Смирновские чтения: материалы Междунар. науч. конф., Москва, 15–17 июня 2017 г.
М.: Современные тетради, 2017.
Similar publications
Global neighbourhood completeness of the Gödel-Löb provability logic
Shamkanov D. S., , in: Logic, Language, Information, and Computation: 24th International Workshop, WoLLIC 2017, London, UK, July 18-21, 2017, Proceedings.: Springer, 2017. P. 358–370.
The Gödel-Löb provability logic GL and establish that ...
Added: September 26, 2017
A realization theorem for the Gödel-Löb provability logic
Shamkanov D. S., Sbornik Mathematics 2016 Vol. 207 No. 9 P. 1344–1360
We present a new justification logic corresponding to the Gödel-Löb provability logic GL and prove the realization theorem connecting these two systems in such a way that all the realizations provided in the theorem are normal. ...
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Franco Montagna’s Work on Provability Logic and Many-valued Logic
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Franco Montagna, a prominent logician and one of the leaders of the Italian school on Mathematical Logic, passed away on February 18, 2015. We survey some of his results and ideas in the two disciplines he greatly contributed along his career: provability logic and many-valued logic. ...
Added: March 13, 2016
Circular proofs for the Gödel–Löb provability logic
Shamkanov D. S., Mathematical notes 2014 Vol. 96 No. 4 P. 575–585
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. ...
Added: August 13, 2014
Interpolation properties for provability logics GL and GLP
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We study interpolation properties of provability logics. We prove the Lyndon interpolation for GL and the uniform interpolation for GLP. ...
Added: February 6, 2013
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