Querying Historical Data Over Multiple Time-Lines

Abstract.

In a temporal database, time-varying relations may be defined over multiple time-lines with varying rates of sampling and/or progress, for instance, multiple time series. There is a need to represent such data in a temporal model and provide query languages. In this paper, we propose a clocked temporal relational algebra, called ${\mathfrak{R}}$, which supports temporal relations based on multiple time-lines. In the underlying model, temporal relations (historical data) are defined over clocks which are subsequences of an assumed global time-line. The algebra is uniform, it is a consistent extension of the relational algebra, and it includes a number of temporal operators to combine data based on different time-lines, as well as extensions of the operators of the relational algebra. The semantics of an operation of ${\mathfrak{R}}$ depends on the clocks of the relations involved in the operation as well as the relations. We outline a formal interpretation of expressions of ${\mathfrak{R}}$, which also represent clocked relations, and sketch a naïve expression evaluation method.