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arXiv · 2605.12351

Proof Theory for Bimodal Provability Logics

Borja Sierra Miranda·Thomas Studer
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Abstract

We provide the first (non-labelled) sequent calculi for bimodal provability logics with "usual" provability predicates. In particular, we introduce calculi for the logics CS, CSM and ER. Additionally, we present non-wellfounded versions of our calculi, and use them to establish a cut-elimination procedure. Finally, we prove the first interpolation results for these logics showing that they all enjoy the uniform Lyndon interpolation property.

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Borja Sierra Miranda, Thomas Studer. 2026-05-12. Proof Theory for Bimodal Provability Logics. https://arxiv.org/abs/2605.12351

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