The problem of integrating information from conflicting sources comes up in many current applications, such as cooperative information systems, heterogeneous databases, and multiagent systems. We model this by the operation of merging first-order theories. We propose a formal semantics for this operation and show that it has desirable properties, including abiding by majority rule in case of conflict and syntax independence. We apply our semantics to the special case when the theories to be merged represent relational databases under integrity constraints. We then present a way of merging databases that have different or conflicting schemas caused by problems such as synonyms, homonyms or type conflicts mentioned in the schema integration literature.