Cut-elimination for the alternation-free modal mu-calculus

Bahareh Afshari; Johannes Kloibhofer

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arXiv · 2510.11293

Cut-elimination for the alternation-free modal mu-calculus

Bahareh Afshari·Johannes Kloibhofer

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Abstract

We present a syntactic cut-elimination procedure for the alternation-free fragment of the modal mu-calculus. Cut reduction is carried out within a cyclic proof system, where proofs are finitely branching but may be non-wellfounded. The structure of such proofs is exploited to directly transform a cyclic proof with cuts into a cut-free one, without detouring through other logics or relying on intermediate machinery for regularisation. Novel ingredients include the use of multicuts and results from the theory of well-quasi-orders, the later used in the termination argument.

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Bahareh Afshari, Johannes Kloibhofer. 2025-10-13. Cut-elimination for the alternation-free modal mu-calculus. https://arxiv.org/abs/2510.11293

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