A Resolution Calculus for First-order Schemata

Vincent Aravantinos (1) , Mnacho Echenim (2) , Nicolas Peltier (2)

1 LIG - Laboratoire d'Informatique de Grenoble
2 CAPP - Calculs algorithmes programmes et preuves

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.

Mots clés: Propositional logic; first-order logic; schemata; resolution calculus

Domaines: Logique en informatique [cs.LO]

Vincent Aravantinos, Mnacho Echenim, Nicolas Peltier. A Resolution Calculus for First-order Schemata. Fundamenta Informaticae, 2013, 125 (2), pp.101-133. ⟨10.3233/FI-2013-855⟩. ⟨hal-00933896⟩