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Martin Amerbauer (1996). Cut-Free Tableau Calculi for Some Propositional Normal Modal Logics.

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  1.  14
    Cut-Elimination for Weak Grzegorczyk Logic Go.Rajeev Goré & Revantha Ramanayake - 2014 - Studia Logica 102 (1):1-27.
    We present a syntactic proof of cut-elimination for weak Grzegorczyk logic Go. The logic has a syntactically similar axiomatisation to Gödel–Löb logic GL (provability logic) and Grzegorczyk’s logic Grz. Semantically, GL can be viewed as the irreflexive counterpart of Go, and Grz can be viewed as the reflexive counterpart of Go. Although proofs of syntactic cut-elimination for GL and Grz have appeared in the literature, this is the first proof of syntactic cut-elimination for Go. The proof is technically interesting, requiring (...)
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    Around Provability Logic.Leo Esakia - 2009 - Annals of Pure and Applied Logic 161 (2):174-184.
    We present some results on algebraic and modal analysis of polynomial distortions of the standard provability predicate in Peano Arithmetic PA, and investigate three provability-like modal systems related to the Gödel–Löb modal system GL. We also present a short review of relational and topological semantics for these systems, and describe the dual category of algebraic models of our main modal system.
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