In order to face this challenge, we have recently proposed a language, called DATALOG(C(not equal)) [5], that extends DATALOG with a restricted form of negation while keeping the good properties of DATALOG, and UCQ, for data exchange. In this article, we provide evidence in favor of the use of DATALOG(C(not equal))as a query language for data exchange systems. More precisely, we introduce the syntax and semantics of DATALOG(C(not equal)), we present some of the fundamental results about this language shown in [5], and we extend those results to the case of data exchange settings that allow for constraints in the target schema. All of these results provide justification for the use of DATALOG(C(not equal)) in practice.