Automated reasoning on monotonic constraints

We study the properties of monotonic parts of (continuous) constraints. We design a general framework to reason about them : directions can be abstracted by signs, which capture significant information on the location of solutions. We show that this formalism is appropriate to study the relative position of solution sets. Efficient algorithms are proposed to diagnose the behaviour of some consistency techniques. These methods raise new perspectives on an open issue: the prediction of the consistency technique to be used wrt a given problem.