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Maritime monitoring systems support safe shipping as they allow for the real-time detection of dangerous, suspicious and illegal vessel activities. We present such a system using the Run-Time Event Calculus, a composite event recognition system with formal, declarative semantics. For effective recognition, we developed a library of maritime patterns in close collaboration with domain experts. We present a thorough evaluation of the system and the patterns both in terms of predictive accuracy and computational efficiency, using real-world datasets of vessel position streams and contextual geographical information.