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arXiv · 2307.06846

A note on the incompleteness of Afshari & Leigh's system Clo

Johannes Kloibhofer
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Abstract

The system $\mathsf{Clo}$ is a cyclic, cut-free proof system for the modal $\mu$-calculus. It was introduced by Afshari & Leigh as an intermediate system in their intent to show the completeness of Kozen's axiomatisation for the modal $\mu$-calculus. We prove that $\mathsf{Clo}$ is incomplete by giving a valid sequent that is not provable in $\mathsf{Clo}$.

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Johannes Kloibhofer. 2023-07-13. A note on the incompleteness of Afshari & Leigh's system Clo. https://arxiv.org/abs/2307.06846

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