Events on the Web are increasingly being produced in the form of data streams, and are present in many different scenarios and applications such as health monitoring, environmental sensing or social networks. The heterogeneity of event streams has raised the challenges of integrating, interpreting and processing them coherently. Semantic technologies have shown to provide both a formal and practical framework to address some of these challenges, producing standards for representation and querying, such as RDF and SPARQL. However, these standards are not suitable for dealing with streams for events, as they do not include the concpets of streaming and continuous processing. The idea of RDF stream processing (RSP) has emerged in recent years to fill this gap, and the research community has produced prototype engines that cover aspects including complex event processing and stream reasoning to varying degrees. However, these existing prototypes often overlook key principles of reactive systems, regarding the event-driven processing, responsiveness, resiliency and scalability. In this paper we present a reactive model for implementing RSP systems, based on the Actor model, which relies on asynchronous message passing of events. Furthermore, we study the responsiveness property of RSP systems, in particular for the delivery of streaming results.