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 Que1 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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The notion of SOLAP (Spatial On-Line Analytical Processing) is aimed at exploring spatial data in the same way as OLAP operates over tables. SOLAP, however, only accounts for discrete spatial data. Current decision support systems are increasingly being needed for handling more complex types of data, like continuous fields, which describe physical phenomena that change continuously in time and/or space (e.g., temperature). Although many models have been proposed for adding spatial (continuous and discrete) information to OLAP tools, no one is general enough to allow users to just perceive data as a cube, and analyze any type of spatial data together with typical alphanumerical discrete OLAP data, using only the classic OLAP operators (e.g., Roll-up, Drill-down). In this paper the authors propose a model and an algebra supporting it, that allow operating over data cubes, independently of the underlying data types and physical data representation. That means, in this approach, the final user only sees the typical OLAP operators at the query level, whereas at lower abstraction levels the authors provide discrete and continuous spatial data support as well as different ways of partitioning the space. As far as the authors are aware of, this is the first proposal, which provides such a general framework for spatiotemporal data analysis.

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