The emergence of event-driven architectures, automation of business processes, drastic cost-reductions in sensor technology, and a growing need to monitor IT systems (as well as other systems) due to legal, contractual, or operational considerations lead to an increasing generation of events. This development is accompanied by a growing demand for managing and processing events in an

automated and systematic way. Complex Event Processing (CEP) encompasses the (automatable) tasks involved in making sense of all events in a system by deriving higher-level knowledge from lower-level events while the events

occur, i.e., in a timely, online fashion and permanently.

At the core of CEP are queries which monitor streams of "simple" events for so-called complex events, that is, events or situations that manifest themselves in certain combinations of several events occurring (or not occurring) over time and that cannot be detected from looking only at single events. Querying events is fundamentally different from traditional querying and reasoning with database or Web data, since event queries are standing queries that are evaluated permanently over time against incoming streams of event data. In order to express complex events that are of interest to a particular application or user in a convenient, concise, cost-effective and maintainable manner, special purpose Event Query Languages (EQLs) are needed.

This thesis investigates practical and theoretical issues related to querying complex events, covering the spectrum from language design over declarative semantics to operational semantics for incremental query evaluation. Its central topic is the development of the high-level event query language XChangeEQ.

In contrast to previous data stream and event query languages, XChangeEQ's language design recognizes the four querying dimensions of data extractions, event composition, temporal relationships, and, for non-monotonic queries involving negation or aggregation, event accumulation. XChangeEQ deals with complex structured data in event messages, thus addressing the need to query events communicated in XML formats over the Web. It supports deductive rules as an abstraction and reasoning mechanism for events. To achieve a full coverage of the four querying dimensions, it builds upon a separation of concerns of the four querying dimensions, which makes it easy-to-use and highly expressive.

A recurrent theme in the formal foundations of XChangeEQ is that, despite the fundamental differences between traditional database queries and event queries, many well-known results from databases and logic programming are, with some importance changes, applicable to event queries. Declarative semantics for XChangeEQ are given as a (Tarski-style) model theory with accompanying fixpoint theory. This approach accounts well for (1) data in events and (2) deductive rules defining new events from existing ones, two aspects often neglected in previous work of semantics of EQLs.

For the evaluation of event queries, this work introduces operational semantics based on an extended and tailored form of relational algebra and query plans with materialization points. Materialization points account for storing and maintaining information about those received events that are relevant for, i.e., can contribute to, future query answers, as well as for an incremental evaluation that avoids recomputing certain intermediate results. Efficient state maintenance in incremental evaluation is approached by "differentiating" algebra expressions, i.e., by deriving expressions for computing only the changes to materialization points. Knowing how long an event is relevant is a prerequisite for performing garbage collection during event query evaluation and also of central importance for developing cost-based query planners. To this end, this thesis introduces a notion of relevance of events (to a given query plan) and develops methods for determining temporal r