A study of cut-elimination for a non-labelled cyclic proof system for propositional dynamic logics

Yukihiro Oda

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arXiv · 2512.15075

A study of cut-elimination for a non-labelled cyclic proof system for propositional dynamic logics

Yukihiro Oda

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Abstract

Dynamic logic is a modal logic for reasoning about programs. A cyclic proof system is a proof system that allows proofs containing cycles and is an alternative to a proof system containing (co-)induction. This paper introduces a sequent calculus and a non-labelled cyclic proof system for an extension of propositional dynamic logic obtained by adding backwards modal operators. We prove the soundness and completeness of these systems and show that cut-elimination fails in both. Moreover, we show the cut-elimination property of the cyclic proof system for propositional dynamic logic obtained by restricting ours.

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Yukihiro Oda. 2025-12-17. A study of cut-elimination for a non-labelled cyclic proof system for propositional dynamic logics. https://arxiv.org/abs/2512.15075

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