A Practical Extension Mechanism for Decision Procedures: the Case Study of Universal Presburger Arithmetic

In this paper, we propose a generic mechanism for extending decision procedures by means of a lemma speculation mechanism. This problem is important in order to widen the scope of decision procedures incorporated in state-of-the-art veri cation systems. Soundness and termination of the extension schema are formally stated and proved. As a case study, we consider extensions of a decision procedure for the quanti er-free fragment of Presburger Arithmetic to signi cant fragments of non-linear arithmetic.