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Sémantique des jeux asynchrones et réécriture 2-dimensionnelle

Abstract : Game semantics characterize the interactive behaviour of proofs and programs, by modeling them as strategies which describe the way they react to their environment. In order to take in account concurrent aspects of proofs in linear logic, usual notions and techniques in game semantics are recasted in an asynchronous and non-alternating framework. In a first part, we define a family of asynchronous strategies giving rise to a model of linear logic, which is fully complete for the multiplicative fragment. These strategies are defined in a purely local way by a series of diagrammatic axioms. Then, they are refined by a dynamic scheduling criterion, which is shown to constrain strategies to satisfy an oriented variant of the correctness criterion of proof nets. This asynchronous formulation unifies various models of linear logic -- sequential as well as concurrent, dynamic as well as static -- where proofs are seen either as sequential strategies, as concurrent strategies, as relations, or as event structures. In a second part, we investigate another approach to describe the causality induced by proofs and introduce a game semantics which captures dependencies induced by first order connectives in propositional logic. We then show that the resulting category can be finitely presented by a 2-polygraph and discuss how this presentation could be oriented in a confluent rewriting system. In particular, we introduce an unification algorithm in this 2-dimensional framework.
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https://tel.archives-ouvertes.fr/tel-00338643
Contributor : Samuel Mimram <>
Submitted on : Tuesday, December 2, 2008 - 10:16:44 PM
Last modification on : Friday, March 27, 2020 - 3:56:19 AM
Long-term archiving on: : Wednesday, March 29, 2017 - 3:28:16 PM

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  • HAL Id : tel-00338643, version 2

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Samuel Mimram. Sémantique des jeux asynchrones et réécriture 2-dimensionnelle. Informatique [cs]. Université Paris-Diderot - Paris VII, 2008. Français. ⟨tel-00338643v2⟩

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