In this paper, we propose to investigate the notion of integrity constraints in inductive databases. We advocate that integrity constraints can be used in this context as an abstract concept to encompass common data mining tasks such as the detection of corrupted data or of patterns that contradict the expert beliefs. To illustrate this possibility we propose a form of constraints called association map constraints to specify authorized confidence variations among the association rules. These constraints are easy to read and thus can be used to write clear specifications. We also present experiments showing that their satisfaction can be tested in practice.