On Constructive Cut Admissibility in Deduction Modulo

Deduction modulo is a theoretical framework which allows the introduction of computational steps in deductive systems. This approach is well suited to automated theorem proving. We describe a proofsearch 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. Then we 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.