This paper is about detecting and segmenting interrelated events which occur in challenging videos with motion blur, occlusions, dynamic backgrounds, and missing observations. We argue that holistic reasoning about time intervals of events, and their temporal constraints is critical in such domains to overcome the noise inherent to low-level video representations. For this purpose, our first contribution is the formulation of probabilistic event logic (PEL) for representing temporal constraints among events. A PEL knowledge base consists of confidence-weighted formulas from a temporal event logic, and specifies a joint distribution over the occurrence time intervals of all events. Our second contribution is a MAP inference algorithm for PEL that addresses the scalability issue of reasoning about an enormous number of time intervals and their constraints in a typical video. Specifically, our algorithm leverages the spanning-interval data structure for compactly representing and manipulating entire sets of time intervals without enumerating them. Our experiments on interpreting basketball videos show that PEL inference is able to jointly detect events and identify their time intervals, based on noisy input from primitive-event detectors.