What is "next" in event processing?

Event processing systems have wide applications ranging from managing events from RFID readers to monitoring RSS feeds. Consequently, there exists much work on them in the literature. The prevalent use of these systems is on-line recognition of patterns that are sequences of correlated events in event streams. Query semantics and implementation efficiency are inherently determined by the underlying temporal model: how events are sequenced (what is the "next" event), and how the time stamp of an event is represented. Many competing temporal models for event systems have been proposed, with no consensus on which approach is best. We take a foundational approach to this problem. We create a formal framework and present event system design choices as axioms. The axioms are grouped into standard axioms and desirable axioms. Standard axioms are common to the design of all event systems. Desirable axioms are not always satisfied, but are useful for achieving high performance. Given these axioms, we prove several important results. First, we show that there is a unique model up to isomorphism that satisfies the standard axioms and supports associativity, so our axioms are a sound and complete axiomatization of associative time stamps in eventsystems. This model requires time stamps with unbounded representations. We present a slightly weakened version of associativity that permits a temporal model with bounded representations. We show that adding the boundedness condition also results in a unique model, so again our axiomatization is sound and complete. We believe this model is ideally suited to be the standard temporal model for complex event processing.