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Pré-Publication, Document De Travail Année : 2024

Linear realisability on untyped nets

Résumé

We present a new realisability model based on orthogonality for Linear Logic in the context of nets-untyped proof structures with generalized axiom. We show that it adequately models second order multiplicative linear logic. As usual, not all realizers are representations of a proof, but we identify specific types (sets of nets closed under bi-othogonality) that capture exactly the proofs of a given sequent thus proving a completeness theorem. Furthermore these types are orthogonal's of finite sets; this ensures the existence of a correctnesss criterion that runs in finite time.
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hal-04432854 , version 1 (06-02-2024)

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  • HAL Id : hal-04432854 , version 1

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Adrien Ragot, Thomas Seiller, Lorenzo Tortora de Falco. Linear realisability on untyped nets. 2024. ⟨hal-04432854⟩
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