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arXiv · 0903.5392

Quasipolynomial Normalisation in Deep Inference via Atomic Flows and Threshold Formulae

Paola Bruscoli·Alessio Guglielmi·Tom Gundersen·Michel Parigot
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Abstract

Jeřábek showed that cuts in classical propositional logic proofs in deep inference can be eliminated in quasipolynomial time. The proof is indirect and it relies on a result of Atserias, Galesi and Pudlák about monotone sequent calculus and a correspondence between that system and cut-free deep-inference proofs. In this paper we give a direct proof of Jeřábek's result: we give a quasipolynomial-time cut-elimination procedure for classical propositional logic in deep inference. The main new ingredient is the use of a computational trace of deep-inference proofs called atomic flows, which are both very simple (they only trace structural rules and forget logical rules) and strong enough to faithfully represent the cut-elimination procedure.

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Paola Bruscoli, Alessio Guglielmi, Tom Gundersen, Michel Parigot. 2016-05-02. Quasipolynomial Normalisation in Deep Inference via Atomic Flows and Threshold Formulae. https://doi.org/10.1007/978-3-642-17511-4_9

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