To be or not to be ... a global constraint

Constraint propagation is widely recognized as a fundamental reasoning component in constraint programming. In the last decade, the concept of "global constraint" has attracted significant attention, since it is critical to achieve reasonable pruning, and efficiency, in many applications. However, even if the name "global constraint" carries a strong intuition in itself, there is no formal definition of this important concept. This paper proposes various notions of globality in order to understand this concept more thoroughly.