In pervasive computing environments, complex event processing has become increasingly important in modern applications. A key aspect of complex event processing is to extract patterns from event streams to make informed decisions in real-time. However, network latencies and machine failures may cause events to arrive out-of-order. In addition, existing literatures assume that events do not have any duration, but events in many real world application have durations, and the relationships among these events are often complex. In this work, we first analyze the preliminaries of time semantics and propose a model of it. A hybrid solution including time-interval to solve out-of-order events is also introduced, which can switch from one level of output correctness to another based on real time. The experimental study demonstrates the effectiveness of our approach.