Abstract
A number of approaches that have been taken to using sets to represent compound values and uncertain information in relational databases. We review three such approaches (collective sets, disjunctive sets and generalized sets), and propose a new approach (restricted cardinality sets), in which every set is accompanied by a range of possible cardinalities of the actual value represented. We show that this approach generalizes the other approaches, leading to a simpler, more flexible representation. We also consider defining algebraic operations on the sets.
on leave from Victoria University of Wellington, Wellington, New Zeland
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Abiteboul, S. and Bodoit, N., Non First Normal Form Relations: An Algebra Allowing Data Restructuring, Rapports de Recherche No.347, Nov. 1984., Institut National de Recherche en Informatique et en Automatique, Domaine de Voluceau, Rocquencourt, B. P. 105, 78153 Le Chesnay Cedex, France.
Arisawa, H., Moriya, K. and Miura, T., “Operations and Properties on Non-First-Normal-Form Relational Databases”, in Proc. of the ACM International Conf. on VLDB, Florence, 1983.
Codd, E. F., “A Relational Model of Data for Large Shared Data Banks”, Commun. of the ACM, Vol.13, No.6, June 1970, pp. 377–387.
Codd, E. F., “Extending the Database Relational Model to Capture More Meaning”, ACM Trans. on Database Systems, Vol.4, No.4, Dec 1979, pp. 397–434.
Date, C. J., An Introduction to Database Systems, Volume 2, Addison-Wesley, 1983.
Delobel, C., “Normalization and Hierarchical Dependencies in the Relational Data Model”, ACM Trans. on Database Systems, Vol.3, 1978.
Fischer, P. C. and Thomas, S., “Operators for Non-First-Normal Form Relations”, Proc. IEEE COMPSAC, 1983, pp.464–475.
Grant, J. and Minker, J., “Answering Queries in Indefinite Databases and the Null Value Problem”, Advances in Computing Research, Vol.3, pp.247–267, 1986.
Jaeschke, G., The Theory of One Attribute Nesting, Heidelberg Scientific Center Technical Note, TN 82.01.
Jaeschke, G. and Schek, H.-J., “Remarks on the Algebra of Non First Normal Form Relations”, Proc. of the SIGACT-SIGMOD Symp. on Principles of Database Systems, Los Angeles, March 1982, pp 124–138.
Kobayashi, I., An Overview of the Database Management Technology, Techn. Report TRCS-4-1, Sanno College, 1753 Kamikasuya, Isehara, Kanagawa 259-11, Japan, June 1980.
Lipski, W. Jr., “On Semantic Issues Connected with Incomplete Information Databases”, ACM Trans. on Database Systems, Vol.4, No.3, Sept 1979, pp.262–296.
Lipski, W. Jr., “On Databases with Incomplete Information”, Journal of ACM, Vol.28, No.1, Jan 1981, pp.41–70.
MacLeod, I. A., “A Model for Integrated Information Systems”, Proc. of the ACM International Conf. on VLDB, Florence, 1983.
Maier, D., The Theory of Relational Databases, Computer Science Press, Rockville, 1983.
Makinouchi, A., “A Consideration on Normal Form of Not-Necessarily-Normalized Relation in the Relational Data Model”, Proc. of the ACM International Conf. on VLDB, Tokyo, October 1977, pp. 447–453.
Michalewicz, Z. and Yeo, A., “Sets in Relational Databases”, Proceedings of the Canadian Information Processing Society, Edmonton, November 1987, pp.237–245.
Michalewicz, Z. and Yeo, A., “Interpreting Sets in Relational Databases”, submitted to Int. Conference on Statistical and Scientific Databases, Rome, June 1988.
Osborn, S. L. and Heaven, T. E., “The Design of a Relational Database System with Abstract Data Types for Domains”, ACM Trans. on Database Systems, Vol.11, No.3, Sept. 1986, pp. 357–373.
Schek, H.-J. and Pistor, P., “Data structure for an integrated data base managment and information retrieval system”, Proc. of the ACM 8th VLDB, 1982.
Schek, H.-J. and Scholl, M. H., “The Relational Model with Relation-Valued Attributes”, Inform. Systems, Vol. 11, No.2, 1986, pp. 137–147.
sSowa, J. F., Conceptual Structures, Addison-Wesley, 1984.
Thomas, S., A Non-First-Normal Form Relational Database Model, Ph.D. Dissertation, Vanderblit University, August 1983.
Ullman, J.D., Principles of Database Systems, Computer Science Press, 2nd edition, 1982.
Vassiliou, Y., “Null Values in Database Management: A Denotational Semantics Approach”, Proc. ACM SIGMOD 1979, Int. Conf. on Manage. of Data, Boston, Mass., May 30–June 1, 1979.
Yeo, A., Sets in Relational Databases, MSc. Thesis, Department of Computer Science, Victoria University, Wellington, New Zealand, 1988.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Michalewicz, Z., Groves, L.J. (1988). Sets and uncertainty in relational databases. In: Bouchon, B., Saitta, L., Yager, R.R. (eds) Uncertainty and Intelligent Systems. IPMU 1988. Lecture Notes in Computer Science, vol 313. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19402-9_65
Download citation
DOI: https://doi.org/10.1007/3-540-19402-9_65
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-19402-6
Online ISBN: 978-3-540-39255-2
eBook Packages: Springer Book Archive