An explicit formula for the free exponential modality of linear logic
Résumé
The exponential modality of linear logic associates a commutative comonoid !A to every formula A, this enabling to duplicate the formula in the course of reasoning. Here, we explain how to compute the free commutative comonoid !A as a sequential limit of equalizers in any symmetric monoidal category where this sequential limit exists and commutes with the tensor product. We apply this general recipe to a series of models of linear logic, typically based on coherence spaces, Conway games and niteness spaces. This algebraic description unies for the rst time the various constructions of the exponential modality in spaces and games. It also sheds light on the duplication policy of linear logic, and its interaction with classical duality and double negation completion.
Domaines
Logique en informatique [cs.LO] Informatique et langage [cs.CL] Topologie algébrique [math.AT] Algèbres quantiques [math.QA] Géométrie algébrique [math.AG] Informatique et théorie des jeux [cs.GT] Logiciel mathématique [cs.MS] Théorie et langage formel [cs.FL] Langage de programmation [cs.PL] Catégories et ensembles [math.CT] Logique [math.LO]| Origine | Fichiers produits par l'(les) auteur(s) |
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