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This paper describes the design of SIENA, an Internet-scale event notification middleware service for distributed event-based applications deployed over wide-area networks. SIENA is responsible for selecting the notifications that are of interest to clients (as expressed in client subscriptions) and then delivering those notifications to the clients via access points. The key design challenge for SIENA is maximizing expressiveness in the selection mechanism without sacrificing scalability of the delivery mechanism. This paper focuses on those aspects of the design of SIENA that fundamentally impact scalability and expressiveness. In particular, we describe SIENA's data model for notifications, the covering relations that formally define the semantics of the data model, the distributed architectures we have studied for SIENA's implementation, and the processing strategies we developed to exploit the covering relations for optimizing the routing of notifications.