9 Octobre - 15 Octobre

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Vendredi 13 Octobre
Heure: 11:00 - 12:30
Lieu: Salle B107, bâtiment B, Université de Villetaneuse
Résumé: Smooth models of Differential Linear Logic
Description: Marie Kerjean Differential Linear Logic was constructed following a study of discrete vectorial models of Linear Logic. We want to extend the semantics of Linear Logic in the natural domain of continuous objects and analysis. From the basic fact that Seely's formulas is the direct interpretation of the Kernel Theorem for distributions, we explain two developments :

On one hand we axiomatize a Smooth Differential Linear Logic with a graded syntax where to each solvable Linear partial differential equation one associate an exponential. We construct a model of nuclear Fréchet/ Df spaces for this syntax.

On the other hand, we argue that the interpretation of the $parr$ as Schwartz's epsilon product should be the cornestone of the construction of a smooth classical model of DiLL. From a first-model of $k$-reflexive spaces, and based on pioneering works by Kriegl, Michor and Meise, we construct a variety of (at least two) new models of DiLL. This part is joint work with Y. Dabrowski.