Circular proofs for the Gödel-Löb provability logic

DOI10.1134/S0001434614090326zbMath1329.03092arXiv1401.4002OpenAlexW3098273402MaRDI QIDQ2343897

Daniyar Shamkanov

Publication date: 11 May 2015

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.4002

zbMATH Keywords

sequent calculusprovability logicLyndon interpolation propertyGödel-Löb logiccircular proofsplit sequent

Mathematics Subject Classification ID

Structure of proofs (03F07) Provability logics and related algebras (e.g., diagonalizable algebras) (03F45)

Related Items (10)

Uniform interpolation from cyclic proofs: the case of modal mu-calculus ⋮ Cyclic hypersequent calculi for some modal logics with the master modality ⋮ Provability multilattice logic ⋮ A realization theorem for the Gödel-Löb provability logic ⋮ On translating Lambek grammars with one division into context-free grammars ⋮ Multicomponent proof-theoretic method for proving interpolation properties ⋮ Unnamed Item ⋮ NON–WELL-FOUNDED DERIVATIONS IN THE GÖDEL-LÖB PROVABILITY LOGIC ⋮ NON-WELL-FOUNDED PROOFS FOR THE GRZEGORCZYK MODAL LOGIC ⋮ Interpolation properties for Sacchetti's logics

Uses Software

• Cyclist

Cites Work

• The modal logic of provability: cut-elimination
• Proof analysis in modal logic
• On modal \(\mu \)-calculus and Gödel-Löb logic
• The modal logic of provability. The sequential approach
• A modal sequent calculus for a fragment of arithmetic
• Modal frame correspondences and fixed-points
• Interpolation properties for provability logics GL and GLP
• VALENTINI’S CUT-ELIMINATION FOR PROVABILITY LOGIC RESOLVED
• On the proof theory of the modal logic for arithmetic provability
• Provability logic—a short introduction
• A PURELY SYNTACTIC AND CUT-FREE SEQUENT CALCULUS FOR THE MODAL LOGIC OF PROVABILITY
• Processes, Terms and Cycles: Steps on the Road to Infinity
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