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Pré-Publication, Document De Travail Année : 2023

Functorial Models of Differential Linear Logic

Résumé

There are two types of duality in Linear Logic. The first one is negation, balancing positive and negative formulas. The second one is the duality between linear and non-linear proofs, made symmetrical by Differential Linear Logic. The first duality has been here since the beginning of Linear Logic and has a significance in terms of proof-search and programming operation. However, the computational content of the second is still to understand. In this paper, we reexpress models of Differential Linear Logic in terms of models of Polarized Linear Logic, hoping to get closer to the understanding of Differential Linear Logic. It formalizes Differentiation in terms of a functor on a coslice category, within the linear-non-linear adjunction models of Linear Logic. It is also a first step in studying models mixing polarization and differentiation, concrete instances of which arise in functional analysis.
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Dates et versions

hal-04292862 , version 1 (17-11-2023)

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  • HAL Id : hal-04292862 , version 1

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Marie Kerjean, Valentin Maestracci, Morgan Rogers. Functorial Models of Differential Linear Logic. 2023. ⟨hal-04292862⟩
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