Equational Theorem Proving Modulo

Abstract

AbstractUnlike other methods for theorem proving modulo with constrained clauses [12, 13], equational theorem proving modulo with constrained clauses along with its simplification techniques has not been well studied. We introduce a basic paramodulation calculus modulo equational theories E satisfying certain properties of E and present a new framework for equational theorem proving modulo E with constrained clauses. We propose an inference rule called Generalized E-Parallel for constrained clauses, which makes our inference system completely basic, meaning that we do not need to allow any paramodulation in the constraint part of a constrained clause for refutational completeness. We present a saturation procedure for constrained clauses based on relative reducibility and show that our inference system including our contraction rules is refutationally complete.