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This paper focuses on the problem of reasoning with information provided by a group of databases which share a common set of rules (deductive rules, integrity constraints). Each database is assumed to be consistent with the rules, but federating them may lead to contradictions.This paper describes a logic of beliefs, based on KD logic, for reasoning with contradictory information provided by several databases. It also presents a theorem prover, associated with this logic. This prover, described as a meta-interpreter of PROLOG allows us to derive formulas of the form: given the databases and the rules, assuming an order of relative reliability between the databases, is a given formula deducible? or, what are the individuals which satisfy a given formula? When the set of rules is not recursive, we prove the correctness of this theorem-prover.