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Réseaux et séquents ordonnés

Abstract : This thesis provides a sequent calculus for linear logic enriched with a non comutative and selfdual connective called "before", in between "par" and "times". It is defined for sequents whose formulae are endowed with a partial order. A proof net calculus, a quotient of the sequent calculus is defined in terms of directed graphs. This calculus enjoys a denotational semantics with coherence spaces, which is preserved under cut eliminatio, a terminating and confluent process. Some needed combinatorial properties of partial orders and proof graphs are established, as well as some properties of the commutative calculus with the MIX rule.
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https://tel.archives-ouvertes.fr/tel-00585634
Contributor : Christian Retoré <>
Submitted on : Wednesday, April 13, 2011 - 3:44:15 PM
Last modification on : Saturday, March 28, 2020 - 2:11:02 AM
Long-term archiving on: : Thursday, July 14, 2011 - 2:47:07 AM

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  • HAL Id : tel-00585634, version 1

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Christian Retoré. Réseaux et séquents ordonnés. Mathématiques [math]. Université Paris-Diderot - Paris VII, 1993. Français. ⟨tel-00585634⟩

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