Towards Automated Reasoning on the Properties of Numerical Constraints

A general approach to improving constraint solving is to take advantage of information on the structure and particularities of the considered constraints. Specific properties can determine the use of customized solvers, or they can be used to improve solver cooperation and propagation strategies. We propose a framework in which properties are seen as abstractions of the underlying constraints, and relate them to the literature on abstract reasoning. We mainly exemplify this framework on numerical constraints, where such properties as monotonicity and convexity are important. In particular, we show how deductions can be made on such constraints to dynamically infer properties. We overview connections with recent works, and we give guidelines and examples on how this kind of tool can be integrated into existing or customized constraintsolvers.