arXiv Open Access 2023

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

Daniyar Shamkanov

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Abstrak

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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math.LO

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Daniyar Shamkanov

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Shamkanov, D. (2023). On structural proof theory of the modal logic K+ extended with infinitary derivations. https://arxiv.org/abs/2310.10309

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Tahun Terbit: 2023
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓