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Logique, Réalisabilité et Concurrence

Abstract : This thesis is devoted to the application of realisability techniques in the study of the computational meaning of logic. In a first part, we recall the formalism of Krivine's classical realisability, in which we carry a study of the operational contents of purely classical tautologies. This exploration of the computational meaning of classical disjunction reveals rich behaviours, with strong interactive intuitions, that are profitably interpreted as typed control structures. In search of a better understanding of the nature of those mechanisms, we then define a similar realisability technique for a model of concurrent computation, in order to build a notion of constructivity that is not based on the idea of function, but rather on that of interactive process. The framework we get provides a genuinely concurrent interpretation of linear logic in a process calculus derived from the pi-calculus, which allows us to apply in the concurrent case the specification methods previously studied in the sequential context. Subsequently, the study of translations of classical logic into linear logic provides systematic reconstructions of interactive decompositions of functional computation, which establishes a link at the logical level between the sequential and concurrent realisabilities. In the last part, we study in more detail the kind of computation inherited from process algebras, in order to understand its kind of scheduling. This study leads us to the definition of a more geometric computation model that allows a formal exploration of the notion of causality in concurrent calculi.
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Contributor : Emmanuel Beffara <>
Submitted on : Thursday, December 15, 2005 - 11:01:04 AM
Last modification on : Saturday, March 28, 2020 - 2:18:42 AM
Long-term archiving on: : Friday, September 14, 2012 - 4:21:31 PM



  • HAL Id : tel-00011205, version 1



Emmanuel Beffara. Logique, Réalisabilité et Concurrence. Mathématiques [math]. Université Paris-Diderot - Paris VII, 2005. Français. ⟨tel-00011205⟩



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