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PREUVES, PROGRAMMES et SYSTÈMES |  |
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PREUVES, PROGRAMMES et SYSTÈMES | |
| HAL: hal-00529320, version 1 |
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| 16th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR-16, Dakar : Senegal (2010) |
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| A Quasipolynomial Cut-Elimination Procedure in Deep Inference via Atomic Flows and Threshold Formulae |
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| Paola Bruscoli 1Alessio Guglielmi 1 |
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| (2010) |
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| 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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| 1: | CALLIGRAMME (INRIA Lorraine - LORIA) |
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INRIA – CNRS : UMR7503 – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL) |
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| 2: | Laboratoire d'informatique de l'école polytechnique (LIX) |
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CNRS : UMR7161 – Polytechnique - X |
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| 3: | Preuves, Programmes et Systèmes (PPS) |
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CNRS : UMR7126 – Université Paris VII - Paris Diderot |
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| Subject | : | Mathematics/Logic |
| hal-00529320, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00529320 | |
| oai:hal.archives-ouvertes.fr:hal-00529320 | |
| From: Michel Parigot | |
| Submitted on: Monday, 25 October 2010 14:01:12 | |
| Updated on: Thursday, 4 November 2010 14:00:17 | |
