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Communication Dans Un Congrès Année : 2023

Linear realisability over nets and second order quantification

Réalisabilité Linéaire dans les réseaux et quantification du second ordre

Résumé

We present a new realisability model for linear logic based on othogonality in the context of nets -- untyped proof structures with generalized axiom. We show that it models adequately 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. Furthermore these types are orthogonal's of finite sets; this ensures the existence of a correctnesss criterion that runs in finite time. In particular in the well known case of multiplicative linear logic, the types capturing the proofs are generated by the tests of Danos-Regnier, we provide - to our knowledge - the first proof of the folklore result which states "test of a formula are proofs of its negation".
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Dates et versions

hal-04131640 , version 1 (16-06-2023)

Identifiants

  • HAL Id : hal-04131640 , version 1

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Adrien Ragot, Thomas Seiller, Lorenzo Tortora de Falco. Linear realisability over nets and second order quantification. Trends in Linear Logic and Applications, Jul 2023, Rome, Italy. ⟨hal-04131640⟩
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