On Constructive Cut Admissibility in Deduction Modulo

Abstract

Deduction Modulo is a theoretical framework that allows the introduction of computational steps in deductive systems. This approach is well suited to automated theorem proving. We describe a proof-search method based upon tableaux for Gentzen’s intuitionistic LJ extended with rewrite rules on propositions and terms . We prove its completeness with respect to Kripke structures. We then give a soundness proof with respect to cut-free LJ modulo. This yields a constructive proof of semantic cut elimination, which we use to characterize the relation between tableaux methods and cut elimination in the intuitionistic case.KeywordsInduction HypothesisAtomic FormulaIntuitionistic LogicSequent CalculusKripke StructureThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.