On Completeness of Historical Relational Query Languages
44 Pages Posted: 15 Oct 2008
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On Completeness of Historical Relational Query Languages
On Completeness of Historical Relational Query Languages
Date Written: March 1993
Abstract
Numerous proposals for extending the relational data model to incorporate the temporaldimension of data have appeared in the past several years. These proposals have differedconsiderably in the way that the temporal dimension has been incorporated both into thestructure of the extended relations of these temporal models, and consequently into theextended relational algebra or calculus that they define. Because of these differences ithas been difficult to compare the proposed models and to make judgments as to which ofthem might in some sense be equivalent or even better. In this paper we define the notions oftemporally grouped and temporally ungrouped historical data models and propose twonotions of historical reIationa1 completeness, analogous to Codd's notion of relationalcompleteness, one for each type of model. We show that the temporally ungrouped modelsare less expressive than the grouped models, but demonstrate a technique for extending theungrouped models with a grouping mechanism to capture the additional semantic powerof temporal grouping. For the ungrouped models we define three different languages, atemporal logic, a logic with explicit reference to time, and a temporal algebra, and showthat under certain assumptions all three are equivalent in power. For the grouped modelswe define a many-sorted logic with variables over ordinary values, historical values, andtimes. Finally, we demonstrate the equivalence of this grouped calculus and the ungroupedcalculus extended with a grouping mechanism. We believe the classification of historicaldata models into grouped and ungrouped provides a useful framework for the comparisonof models in the literature, and furthermore the exposition of equivalent languages for eachtype provides reasonable standards for common, and minimal, notions of historical relationalcompleteness.
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