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In information systems, one often has to deal with constraints in order to compel the semantics and integrity of the stored information or to express some querying criteria. Hereby, different constraints can be of different importance. A method to aggregate the information about the satisfaction of a finite number of constraints for a given data instance is presented. Central to the proposed method is the use of extended possibilistic truth values (to express the degree of satisfaction of a constraint) and the use of residual implicators and residual coimplicators (to model the impact and relevance of a constraint). The proposed method can be applied to any constraint-based system. A database application is discussed and illustrated.