Numerous proposals for extending the relational data model to incorporate the temporal
dimension of data have appeared in the past several years. These proposals have differed
considerably in the way that the temporal dimension has been incorporated both into the
structure of the extended relations of these temporal models, and consequently into the
extended relational algebra or calculus that they define. Because of these differences it has
been difficult to compare the proposed models and to make judgments as to which of them
might in some sense be equivalent or even better. In this paper we define the notions of
temporally grouped and temporally ungrouped historical data models and propose
two notions of historical relational completeness, analogous to Codd's notion of relational
completeness, one for each type of model. We show that the temporally ungrouped
models are less powerful than the grouped models, but demonstrate a technique for extending
the ungrouped models with a grouping mechanism to capture the additional semantic
power of temporal grouping. For the ungrouped models we define three different languages,
a temporal logic, a logic with explicit reference to time, and a temporal algebra, and show
that under certain assumptions all three are equivalent in power. For the grouped models
we define a many-sorted logic with variables over ordinary values, historical values, and
times. Finally, we demonstrate the equivalence of this grouped calculus and the ungrouped
calculus extended with the proposed grouping mechanism. We believe the classification of
historical data models into grouped and ungrouped provides a useful framework for the
comparison of models in the literature, and furthermore the exposition of equivalent languages
for each type provides reasonable standards for common, and minimal, notions of
historical relational completeness.Information Systems Working Papers Serie