This paper defines new constructs to support aggregation in the temporal query language TQuel and presents their formal semantics in the tuple relational calculus. A formal semantics for Quel aggregates is defined in the process. Multiple aggregates; aggregates appearing in the where, when, and valid clauses; nested aggregation; and instantaneous, cumulative, moving window, and unique variants are supported. These aggregates provide a rich set of statistical functions that range over time, while requiring minimal additions to TQuel and its semantics. We show how the aggregates may be supported in an historical algebra, both in a batch and in an incremental fashion, demonstrating that implementation is straightforward and efficient.
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