In this paper, we propose to use one of the well-known general theories of time and change, namely the Event Calculus (Kowalski and Sergot, New Generation Computing 4, 67-95, 1986), to represent temporal aspects in intelligent medical monitoring systems. In particular, we explore the application of CEC (Chittaro and Montanari, Computational Intelligence 12, 359-382, 1996) (an efficient implementation of the Event Calculus) to the management of mechanical ventilation. First, we present the prototype we have built, which has been extensively tested on patient's data from real clinical cases. Then, we provide a thorough evaluation of the obtained results, pointing out both strengths and weaknesses of the approach, and identifying a number of extensions which can be extremely useful to scale up the medical application of the approach.