A constraint-propagation approach to quantified constraints

Some complex problems could be tackled more satisfactorily by constraint programming tools if it were possible to state arbitrarily quantified constraints. Real-valued quantified constraints have been considered in the field of mathematical programming for more than fifty years, while discrete (boolean) quantified constraints have recently received attention from the SAT community. No direct connection was made between these two research topics, but both of them recently benefited from constraint propagation technology in some sense. It can be hoped for that constraint-propagation will provide a common framework for these two problems. The purpose of this note is to give a brief, non-technical overview of the use of quantified constraints. We briefly present the technique called quantified arc-consistency which we proposed in [BM02] as a generalization of arc-consistency for arbitrarily quantified constraints. 1 Quantified constraints over discrete and continuous