A Quasipolynomial Cut-Elimination Procedure in Deep Inference via Atomic Flows and Threshold Formulae

Abstract : Jerabek showed in 2008 that cuts in propositional-logic deep inference proofs can be eliminated in quasipolynomial time. The proof is an indirect one relying on a result of Atserias, Galesi and Pudlak about monotone sequent calculus and a correspondence between this system and cut-free deep-inference proofs. In this paper we give a direct proof of Jerabek's result: we give a quasipolynomial-time cut-elimination procedure in propositional-logic 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 trace only structural rules and forget logical rules) and strong enough to faithfully represent the cut-elimination procedure.
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https://hal.archives-ouvertes.fr/hal-00529320
Contributor : Michel Parigot <>
Submitted on : Monday, October 25, 2010 - 2:01:12 PM
Last modification on : Thursday, April 4, 2019 - 1:28:48 AM

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  • HAL Id : hal-00529320, version 1

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Paola Bruscoli, Alessio Guglielmi, Tom Gundersen, Michel Parigot. A Quasipolynomial Cut-Elimination Procedure in Deep Inference via Atomic Flows and Threshold Formulae. 16th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR-16, 2010, Dakar, Senegal. Springer, 6355, pp.00-00, 2010, Lecture Notes in Artificial Intelligence. 〈hal-00529320〉

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