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There is a new trend to use Datalog-style rule-based languages to specify modern distributed applications, notably on the Web. We introduce here such a language for a distributed data model where peers exchange messages (i.e. logical facts) as well as rules. The model is formally defined and its interest for distributed data management is illustrated through a variety of examples. A contribution of our work is a study of the impact on expressiveness of "delegations" (the installation of rules by a peer in some other peer) and explicit timestamps. We also validate the semantics of our model by showing that under certain natural conditions, our semantics converges to the same semantics as the centralized system with the same rules. Indeed, we show this is even true when updates are considered.