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arXiv · 2310.10309

On structural proof theory of the modal logic K+ extended with infinitary derivations

Daniyar Shamkanov
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Abstract

We consider an extension of the modal logic of transitive closure K+ with some inifinitary derivations and present a sequent calculus for this extension, which allows non-well-founded proofs. For the given calculus, we obtain the cut-elimination theorem following the lines of so called continuous cut elimination. Our consideration also covers ordinary proofs of K+ since they correspond to cyclic cut-free proofs of the presented sequent calculus.

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Daniyar Shamkanov. 2023-10-16. On structural proof theory of the modal logic K+ extended with infinitary derivations. https://doi.org/10.1093/jigpal%2Fjzae121

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