Recently there has been an increasing interest in integrity constraints associated with relational databases and in inconsistent databases, i.e. databases which do not satisfy integrity constraints. In the presence of inconsistencies two main techniques have been proposed: compute repairs, i.e. minimal set of insertion and deletion operations, called database repairs, and compute consistent answers, i.e. identify the sets of atoms which we can assume true, false and undefined without modifying the database. In this paper feasibility conditions and preference criteria are introduced which, associated with integrity constraints, allow to restrict the number of repairs and to increase the power of queries over inconsistent databases. Moreover, it is studied the complexity of computing repairs and the expressive power of relational queries over databases with integrity constraints, feasibility conditions and preference criteria.
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