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For several reasons databases may become inconsistent with respect to a given set of integrity constraints (ICs): (a) The DBMS have no mechanism to maintain certain classes of ICs. (b) New constraints are imposed on preexisting, legacy data. (c) The ICs are soft, user, or informational constraints that are considered at query time, but without being necessarily enforced. (d) Data from different and autonomous sources are being integrated, in particular in mediator-based approaches.
Leopoldo Bertossi (Thu,) studied this question.