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arXiv · 2203.01600

A theory of cut-restriction: first steps

Agata Ciabattoni·Timo Lang·Revantha Ramanayake
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Abstract

Cut-elimination is the bedrock of proof theory. It is the algorithm that eliminates cuts from a sequent calculus proof that leads to cut-free calculi and applications. Cut-elimination applies to many logics irrespective of their semantics. Such is its influence that whenever cut-elimination is not provable in a sequent calculus the invariable response has been a move to a richer proof system to regain it. In this paper we investigate a radically different approach to the latter: adapting age-old cut-elimination to restrict the shape of the cut-formulas when elimination is not possible. We tackle the "first level" above cut-free: analytic cuts. Our methodology is applied to the sequent calculi for bi-intuitionistic logic and S5 where analytic cuts are already known to be required. This marks the first steps in a theory of cut-restriction.

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Agata Ciabattoni, Timo Lang, Revantha Ramanayake. 2022-03-03. A theory of cut-restriction: first steps. https://arxiv.org/abs/2203.01600

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