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| HAL: hal-00387452, version 1 |
| arXiv: 0905.4064 |
| DOI: 10.1016/j.entcs.2009.07.095 |
| Detailed view |  Export this paper |
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| MFPS 2009, Oxford : Royaume-Uni (2009) |
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| Contraction-free proofs and finitary games for Linear Logic |
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| André Hirschowitz 1Michel Hirschowitz 2, 3 |
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| (2009) |
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| In the standard sequent presentations of Girard's Linear Logic (LL), there are two "non-decreasing" rules, where the premises are not smaller than the conclusion, namely the cut and the contraction rules. It is a universal concern to eliminate the cut rule. We show that, using an admissible modification of the tensor rule, contractions can be eliminated, and that cuts can be simultaneously limited to a single initial occurrence. This view leads to a consistent, but incomplete game model for LL with exponentials, which is finitary, in the sense that each play is finite. The game is based on a set of inference rules which does not enjoy cut elimination. Nevertheless, the cut rule is valid in the model. |
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| 1: | Laboratoire Jean Alexandre Dieudonné (JAD) |
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CNRS : UMR6621 – Université Nice Sophia Antipolis [UNS] |
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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: | Laboratoire d'Intégration des Systèmes et des Technologies (LIST) |
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| 4: | Laboratoire de Mathématiques (LAMA) |
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CNRS : UMR5127 – Université de Savoie |
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| Subject | : | Computer Science/Logic in Computer Science Mathematics/Logic |
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| Linear logic – Game semantics – Contraction elimination |
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| hal-00387452, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00387452 | |
| oai:hal.archives-ouvertes.fr:hal-00387452 | |
| From: Tom Hirschowitz | |
| Submitted on: Monday, 25 May 2009 14:20:10 | |
| Updated on: Friday, 4 September 2009 16:39:56 | |
