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PREUVES, PROGRAMMES et SYSTÈMES |  |
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PREUVES, PROGRAMMES et SYSTÈMES | |
| HAL: hal-00698973, version 1 |
| DOI: 10.1016/j.apal.2011.09.001 |
| Detailed view |  Export this paper |
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| Annals of Pure and Applied Logic 163, 3 (2011) 238-265 |
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| Visible acyclic differential nets, Part I: Semantics |
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| Michele Pagani 1, 2 |
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| (2011-10-10) |
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| We give a geometric condition that characterizes the differential nets having a finitary interpretation in finiteness spaces: visible acyclicity. This is based on visible paths, an extension to differential nets of a class of paths we introduced in the framework of linear logic nets. The characterization is then carried out as follows: the differential nets having no visible cycles are exactly those whose interpretation is a finitary relation. Visible acyclicity discloses a new kind of correctness for the promotion rule of linear logic, which goes beyond sequent calculus correctness. |
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| 1: | Laboratoire d'informatique de Paris-nord (LIPN) |
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CNRS : UMR7030 – Université Paris XIII - Paris Nord |
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| 2: | Preuves, Programmes et Systèmes (PPS) |
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CNRS : UMR7126 – Université Paris VII - Paris Diderot |
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| Subject | : | Computer Science/Logic in Computer Science |
| hal-00698973, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00698973 | |
| oai:hal.archives-ouvertes.fr:hal-00698973 | |
| From: Michele Pagani | |
| Submitted on: Friday, 18 May 2012 14:57:39 | |
| PDF file(s) available on: 2014-05-18 | |
| Updated on: Friday, 18 May 2012 15:55:42 | |
