Event notification services, or alerting services, are used in various applications such as digital libraries, stock tickers, traffic control, or facility management. However, to our knowledge, a common semantics of events in event notification services has not been defined so far. In this paper, we propose a parameterized event algebra which describes the semantics of composite events for event notification systems. We define the event operators that form composite events and we introduce parameters for event instance selection and event instance consumption. These parameters serve as a support for handling duplicates in both primitive and composite events. The event algebra is exemplified in the domain of transportation logistics.