This paper addresses the problem of querying several databases considered as a whole. Assuming that the different databases share a common data description language, the problem that arises is to consistently answer queries even if the database contents are contradictory. The main contribution of this paper is the specification of a query-evaluator for answering closed and open general queries addressed to several databases and for providing explanations about the results. For doing so, we first specify a query-evaluator, in logic, which (...) assumes that the databases are propositional ones and do not contain disjunctions. Then we extend it to first-order databases defined by an extensional part and an intensional part. We also show that the query-evaluator corresponds to a majority merging of the databases. (shrink)