Communication Dans Un Congrès Année : 2025

On the denotation of circular and non-wellfounded proofs in linear logic with fixed points

Résumé

This paper investigates the denotational invariants of non-wellfounded and circular proofs of linear logic with least and greatest fixed points, µLL, by providing a categorical semantics. More precisely the paper successively introduces semantics for (i) non-wellfounded pre-proofs, be they valid or not, (ii) valid pre-proofs exploiting their validity condition by considering an orthogonality construction on the given categorical model and finally (iii) circular strongly valid pre-proofs, exploiting both validity and regularity in order to define inductively the interpretation. Then the paper investigates the semantical content of the translation from finitary proofs to non-wellfounded proofs and, conversely, from (strongly valid) circular proofs to finitary proofs, showing that both translations preserve the interpretation.

Fichier principal
Vignette du fichier
main.pdf (807.34 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-05245059 , version 1 (08-09-2025)

Licence

Identifiants

  • HAL Id : hal-05245059 , version 1

Citer

Thomas Ehrhard, Farzad Jafarrahmani, Alexis Saurin. On the denotation of circular and non-wellfounded proofs in linear logic with fixed points. Logic in Computer Science (LICS) 2025, The 40th ACM, Association for Computing Machinery / IEEE Symposium, Jun 2025, Singapoore, Singapore. ⟨hal-05245059⟩
71 Consultations
138 Téléchargements

Partager

  • More