Chiralities in topological vector spaces

Marie Kerjean 1, 2
2 GALLINETTE - Gallinette : vers une nouvelle génération d'assistant à la preuve
Inria Rennes – Bretagne Atlantique , LS2N - Laboratoire des Sciences du Numérique de Nantes
Abstract : Chiralities are categories introduced by Mellies to account for a game semantics point of view on negation. Here, we uncover instances of this structure in the theory of topological vector spaces, thus constructing several new polarized models of Multiplicative Linear Logic. These models improve previously known smooth models of Differential Linear Logic, showing the relevance of chiralities to express topological properties of vector spaces. They are the first denotational polarized models of Multiplicative Linear Logic, based on the pre-existing theory of topological vector spaces, in which two distinct sets of formulas, two distinct negations, and two shifts appear naturally.
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Submitted on : Sunday, October 27, 2019 - 8:44:44 PM
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Marie Kerjean. Chiralities in topological vector spaces. 2019. ⟨hal-02334917v1⟩

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