Finite domain bounds consistency revisited

A widely adopted approach to solving constraint satisfaction problems combines systematic tree search with constraint propagation for pruning the search space. Constraint propagation is performed by propagators implementing a certain notion of consistency. Bounds consistency is the method of choice for building propagators for arithmetic constraints and several global constraints in the finite integer domain. However, there has been some confusion in the definition of bounds consistency and of bounds propagators. We clarify the differences among the three commonly used notions of bounds consistency in the literature. This serves as a reference for implementations of bounds propagators by defining (for the first time) the a priori behavior of bounds propagators on arbitrary constraints.