The objective of this paper is to investigate the problems related to the extensional integration of information sources. In particular, we propose an approach for managing inconsistent databases, i.e. databases violating integrity constraints. The presence of inconsistent data can be resolved by “repairing” the database, i.e. by providing a computational mechanism that ensures obtaining consistent “scenarios” of the information or by consistently answer to queries posed on an inconsistent set of data. In this paper we consider preferences among repairs and possible answers by introducing a partial order among them on the base of some preference criteria. More specifically, preferences are expressed by considering polynomial functions applied to repairs and returning real numbers. The goodness of a repair is measured by estimating how much it violates the desiderata conditions and a repair is preferred if it minimizes the value of the polynomial function used to express the p...