On Completeness of Historical Relational Query Languages

44 Pages Posted: 15 Oct 2008

See all articles by James Clifford

James Clifford

affiliation not provided to SSRN

Albert Croker

City University of New York (CUNY) - Paul H. Chook Department of Information Systems & Statistics

Alexander Tuzhilin

New York University (NYU) - Leonard N. Stern School of Business; New York University (NYU) - Department of Information, Operations, and Management Sciences

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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.

Suggested Citation

Clifford, James and Croker, Albert and Tuzhilin, Alexander, On Completeness of Historical Relational Query Languages (March 1993). NYU Working Paper No. 2451/14245, Available at SSRN: https://ssrn.com/abstract=1284866

James Clifford

affiliation not provided to SSRN

Albert Croker

City University of New York (CUNY) - Paul H. Chook Department of Information Systems & Statistics ( email )

17 Lexington Avenue
New York, NY 10010
United States

Alexander Tuzhilin

New York University (NYU) - Leonard N. Stern School of Business ( email )

44 West 4th Street
Suite 9-160
New York, NY NY 10012
United States

New York University (NYU) - Department of Information, Operations, and Management Sciences

44 West Fourth Street
New York, NY 10012
United States

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