A realization theorem for the Gödel-Löb provability logic. (English. Russian original) Zbl 06678891

Sb. Math. 207, No. 9, 1344-1360 (2016); translation from Mat. Sb. 207, No. 9, 171-190 (2016).
Summary: We present a new justification logic corresponding to the Gödel-Löb provability logic \(\mathsf{GL}\) and prove the realization theorem connecting these two systems in such a way that all the realizations provided in the theorem are normal.


03B42 Logics of knowledge and belief (including belief change)
03F07 Structure of proofs
03F45 Provability logics and related algebras (e.g., diagonalizable algebras)
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[1] Artemov S. N. 2001 Explicit provability and constructive semantics Bull. Symbolic Logic7 1-36 · Zbl 0980.03059
[2] Ghari M. 2012 PhD thesis
[3] Sambin G. and Valentini S. 1980 A modal sequent calculus for a fragment of arithmetic Studia Logica39 245-256 · Zbl 0457.03016
[4] Sambin G. and Valentini S. 1982 The modal logic of provability. The sequential approach J. Philos. Logic11 311-342 · Zbl 0523.03014
[5] Leivant D. 1981 On the proof theory of the modal logic for arithmetic provability J. Symbolic Logic46 531-538 · Zbl 0464.03019
[6] Ghari M. 2011 Explicit Gödel-Löb provability logic Proceedings of the 42nd Annual Iranian Mathematics Conference 911-914
[7] Kuznets R. 2008 PhD thesis City Univ. of New York
[8] Shamkanov D. S. 2014 Circular Proofs for the Gödel-Löb Provability Logic Mat. Zametki96 609-622 · Zbl 1329.03092
[9] Fitting M. 2009 Realizations and LP Ann. Pure Appl. Logic161 368-387 · Zbl 1221.03020
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