A purely syntactic and cut-free sequent calculus for the modal logic of provability - HAL-SHS - Sciences de l'Homme et de la Société Accéder directement au contenu
Article Dans Une Revue The review of symbolic logic Année : 2009

A purely syntactic and cut-free sequent calculus for the modal logic of provability

Résumé

In this paper we present a sequent calculus for the modal propositional logic GL (the logic of provability) obtained by means of the tree-hypersequent method, a method in which the metalinguistic strength of hypersequents is improved, so that we can simulate trees shapes. We prove that this sequent calculus is sound and complete with respect to the Hilbert-style system GL, that it is contraction free and cut free and that its logical and modal rules are invertible. No explicit semantic element is used in the sequent calculus and all the results are proved in a purely syntactic way.

Mots clés

Fichier principal
Vignette du fichier
articologl5.pdf (245.43 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

halshs-00775808 , version 1 (26-06-2018)

Identifiants

  • HAL Id : halshs-00775808 , version 1

Citer

Francesca Poggiolesi. A purely syntactic and cut-free sequent calculus for the modal logic of provability. The review of symbolic logic, 2009, 2 (4), pp.593-611. ⟨halshs-00775808⟩
62 Consultations
356 Téléchargements

Partager

Gmail Facebook X LinkedIn More