A Resolution Calculus for First-order Schemata

Article type: Research Article

Authors: Aravantinos, Vincent | Echenim, Mnacho | Peltier, Nicolas

Affiliations: LIG/CNRS, Grenoble, France. Vincent.Aravantinos@imag.fr | LIG/Grenoble INP-Ensimag, France. Mnacho.Echenim@imag.fr | LIG/CNRS, Grenoble, France. Nicolas.Peltier@imag.fr

Note: [] Address for correspondence: LIG, 220, rue de la Chimie 38400 Saint Martin d'Hères, France

Abstract: We devise a resolution calculus that tests the satisfiability of infinite families of clause sets, called clause set schemata. For schemata of propositional clause sets, we prove that this calculus is sound, refutationally complete, and terminating. The calculus is extended to first-order clauses, for which termination is lost, since the satisfiability problem is not semi-decidable for nonpropositional schemata. The expressive power of the considered logic is strictly greater than the one considered in our previous work.

Keywords: Propositional logic, first-order logic, schemata, resolution calculus

DOI: 10.3233/FI-2013-855

Journal: Fundamenta Informaticae, vol. 125, no. 2, pp. 101-133, 2013