In streaming applications, it is often required to detect situations of interest, by means of temporal pattern matching, with minimal latency. In the maritime domain, e.g., where it is crucial to prevent activities that are harmful to the environment, we need to report illegal fishing activities, based on streams of low-level vessel actions, as soon as possible. Streams often include events with delayed effects. In multi-agent voting protocols, e.g., a proposed motion may be seconded at the latest by some time in the future. In simulations of biological systems, a signal may lead to the deactivation of the functions of a gene after a time delay. We propose a formal computational framework that handles streams including events with delayed effects. We present the syntax, semantics and reasoning algorithms of our proposed framework, and demonstrate its correctness and complexity. Furthermore, we present a reproducible analysis on large synthetic and real data streams, from the fields of composite event recognition, multi-agent systems and biological feedback processes, and compare the efficiency of our approach with state-of-the-art systems that can perform stream reasoning in these domains. Our results demonstrate that our framework is capable of reasoning over very large streams, including events with delayed effects, while outperforming the state-of-the-art, often by orders of magnitude.
