Linking Focusing and Resolution with Selection

Abstract : Focusing and selection are techniques that shrink the proof search space for respectively sequent calculi and resolution. To bring out a link between them, we generalize them both: we introduce a sequent calculus where each occurrence of an atom can have a positive or a negative polarity; and a resolution method where each literal, whatever its sign, can be selected in input clauses. We prove the equivalence between cut-free proofs in this sequent calculus and derivations of the empty clause in that resolution method. Such a generalization is not semi-complete in general, which allows us to consider complete instances that correspond to theories of any logical strength. We present three complete instances: first, our framework allows us to show that ordinary focusing corresponds to hyperresolution and semantic resolution; the second instance is deduction modulo theory and the related framework called superdeduction; and a new setting, not captured by any existing framework, extends deduction modulo theory with rewriting rules having several left-hand sides, which restricts even more the proof search space.
Type de document :
Pré-publication, Document de travail
2018
Liste complète des métadonnées

https://hal.inria.fr/hal-01670476
Contributeur : Guillaume Burel <>
Soumis le : vendredi 27 avril 2018 - 12:12:21
Dernière modification le : dimanche 29 avril 2018 - 01:11:46

Fichier

lipics.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01670476, version 3

Citation

Guillaume Burel. Linking Focusing and Resolution with Selection. 2018. 〈hal-01670476v3〉

Partager

Métriques

Consultations de la notice

154

Téléchargements de fichiers

50