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Traditional ways of storing and querying data do not work well in scenarios where data is being generated continuously and quick decisions need to be taken. For example, in hospital intensive care units, signals from multiple devices need to be monitored and the occurrence of any anomaly should raise alarms immediately. A typical design would take the average from a window of say 10 seconds (time-based) or 10 successive (count-based) readings and look for sudden deviations. Existing stream processing systems either restrict the windows to time or count-based windows or let users define customized windows in imperative programming languages. These are subject to the implementers' interpretation of what is desired and hard to understand for others. We introduce a formalism for specifying windows based on Monadic Second Order logic. It offers several advantages over ad-hoc definitions written in imperative languages. We demonstrate four such advantages. First, we illustrate how practical streaming data queries can be easily written with precise semantics. Second, we can get different but expressively equivalent formalisms for defining windows. We use one of them (regular expressions) to design an end-user-friendly language for defining windows. Third, we use another expressively equivalent formalism (automata) to design a processor that automatically generates windows according to specifications. The fourth advantage we demonstrate is more sophisticated. Some window definitions have the problem of too many windows overlapping with each other, overwhelming the processing engine. This is handled in different ways by different engines, but all the options are about what to do when this happens at runtime. We study this as a static analysis question and prove that it is undecidable to check whether such a scenario can ever arise for a given window definition. We identify a decidable fragment...