This paper investigates the problem of data integration among Peer-to-Peer (P2P) deductive databases and presents a declarative semantics that generalizes previous proposals in the literature. Basically, by following the classical approach, the objective of a generic peer, joining a P2P system, is to enrich its knowledge by importing as much knowledge as possible while preventing inconsistency anomalies. This basic idea is extended in the present paper by allowing each peer to select between two different settings. It can either declare its local database to be sound but not complete, or declare it to be unsound. In the first case the peer considers its own knowledge more trustable than the knowledge imported from the rest of the system i.e. it gives preference to its knowledge with respect to the knowledge that can be imported from other peers. In the second case the peer considers its own knowledge as trustable as the knowledge that can be imported from the rest of the system i.e. it does not give any preference to its knowledge with respect to the knowledge that can be imported from other peers.