Focus-style proof systems and interpolation for the alternation-free μ-calculus

03/02/2021

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by   Johannes Marti, et al.

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In this paper we introduce a cut-free sequent calculus for the alternation-free fragment of the modal μ-calculus. This system allows for cyclic proofs and uses a simple focus mechanism to control the unravelling of fixpoints along infinite branches. We show that the proof system is sound and complete and apply it to prove that the alternation-free fragment has the Craig interpolation property.