Combining decision procedures

Abstract. We give a detailed survey of the Nelson-Oppen method for combining decision procedures, we show how Shostak's method can be seen as an instance of the Nelson-Oppen method, and we provide a generalization of the Nelson-Oppen method to the case of non-disjoint theories. 1 Introduction Decision procedures are algorithms that can reason about the validity or satisfiability of classes of formulae in a given decidable theory, and always terminate with a positive or negative answer