Sequent Calculi for Nominal Tense Logics: A Step Towards Mechanization?

Stéphane Demri (1, 2)

1 CNRS - Centre National de la Recherche Scientifique
2 Leibniz - IMAG - Laboratoire Leibniz

We define sequent-style calculi for nominal tense logics characterized by classes of modal frames that are first-order definable by certain Π10-formulae and Π20-formulae. The calculi are based on d’Agostino and Mondadori’s calculus KE and therefore they admit a restricted cut-rule that is not eliminable. A nice computational property of the restriction is, for instance, that at any stage of the proof, only a finite number of potential cut-formulae needs to be taken under consideration. Although restrictions on the proof search (preserving completeness) are given in the paper and most of them are theoretically appealing, the use of those calculi for mechanization is however doubtful. Indeed, we present sequent calculi for fragments of classical logic that are syntactic variants of the sequent calculi for the nominal tense logics.

Mots clés: modal logic; sequent-style proof system; nominal tense logic; frame condition; Pi_1^0 formula

Domaines: Informatique [cs]; Logique en informatique [cs.LO]; Intelligence artificielle [cs.AI]

Stéphane Demri. Sequent Calculi for Nominal Tense Logics: A Step Towards Mechanization?. International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX'99), Jun 1999, Saratoga Springs, United States. pp.140-155, ⟨10.1007/3-540-48754-9_15⟩. ⟨hal-03195331⟩