An Abstraction Framework for Soft Constraints and Its Relationship with Constraint Propagation

Soft constraints are very flexible and expressive. However, they also are very complex to handle. For this reason, it may reasonable in several cases to pass to an abstract version of a given soft problem, and then to bring some useful information from the abstract problem to the concrete one. This will hopefully make the search for a solution, or for an optimal solution, of the concrete problem, faster. In this paper we review the main concepts and properties of our abstraction framework for soft constraints, and we show how it can be used to import constraint propagation algorithms from the abstract scenario to the concrete one. This may be useful when we don’t have any (or any efficient) propagation algorithm in the concrete setting.