Algebraic query languages on temporal databases with multiple time granularities

This paper investigates algebraic query languages on temporal databases. The data model used is a multidimensional extension of the temporal modules introduced in [WJS95]. In a multidimensional temporal module, every non-temporal fact has a timestamp that is a set of n-ary tuples of time points. A temporal module has a set of timestamped facts and has an associated temporal granularity (or temporal type), and a temporal database is a set of multidimensional temporal modules with possibly different temporal types. Temporal algebras are proposed on this database model. Example queries and results of the paper show that the algebras are rather expressive. The operations of the algebras are organized into two groups: snapshot-wise operations and timestamp operations. Snapshot-wise operations are extensions of the traditional relational algebra operations, while timestamp operations are extensions of first-order mappings from timestamps to timestamps. Multiple temporal types are only dealt with by these timestamp operations. Hierarchies of algebras are defined in terms of the dimensions of the temporal modules in the intermediate results. The symbol TALG k is used to denote all the algebra queries whose input, output and intermediate modules are of dimensions at mostm, n and k, respectively. (Most temporal algebras proposed in the literature are in TALG 1 .) Equivalent hierarchies TCALC m;n k are defined in a calculus query language that is formulated by using a first-order logic with linear order. The addition of aggregation functions into the algebras is also studied. This work was partly supported by the NSF grant IRI-9409769 and also by an ARPA grant, administered by the Office of Naval Research under grant number N0014-92-J-4038.