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A recursive temporal algebra and temporal completeness
 Proceedings of the Third International Workshop on Temporal Representation and Reasoning (TIME’96
, 1996
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A Temporal Algebra with Recursive Equations
, 1995
"... This paper introduces a recursive temporal algebra for querying timevarying data. The algebra, called ! , is based on a temporal relational data model in which a temporal database is modeled as a collection of timevarying relations. Each timevarying relation is a collection of ordinary relatio ..."
Abstract

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This paper introduces a recursive temporal algebra for querying timevarying data. The algebra, called ! , is based on a temporal relational data model in which a temporal database is modeled as a collection of timevarying relations. Each timevarying relation is a collection of ordinary relations indexed by moments in time. In ! , recursive queries (such as the transitive closure of a given relation) can be formulated through equations. It is shown that other forms of recursion, such as linear recursion, can also be expressed using iteration through time. The meaning of recursive equations is formulated using a standard approach based on fixedpoint semantics. Temporal completeness of ! with bounded time is established, with respect to two other temporal algebras based on temporal semantics which also offer linear recursive operators. Keywords: Temporal databases, temporal algebras, timevarying relations, recursive queries, recursive equations, fixedpoint semantics, linea...