Advertisement

Sets and uncertainty in relational databases

  • Zbigniew Michalewicz
  • Lindsay J. Groves
Intelligent Data Base
Part of the Lecture Notes in Computer Science book series (LNCS, volume 313)

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.

Keywords

Database System Relational Database Incomplete Information Algebraic Operation Attribute Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Abiteboul & Bodoit, 1984]
    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.Google Scholar
  2. [Arisawa, 1983]
    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.Google Scholar
  3. [Codd, 1970]
    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.Google Scholar
  4. [Codd, 1979]
    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.Google Scholar
  5. [Date, 1983]
    Date, C. J., An Introduction to Database Systems, Volume 2, Addison-Wesley, 1983.Google Scholar
  6. [Delobel, 1978]
    Delobel, C., “Normalization and Hierarchical Dependencies in the Relational Data Model”, ACM Trans. on Database Systems, Vol.3, 1978.Google Scholar
  7. [Fisher & Thomas, 1983]
    Fischer, P. C. and Thomas, S., “Operators for Non-First-Normal Form Relations”, Proc. IEEE COMPSAC, 1983, pp.464–475.Google Scholar
  8. [Grant & Minker, 1986]
    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.Google Scholar
  9. [Jaeschke, 1982]
    Jaeschke, G., The Theory of One Attribute Nesting, Heidelberg Scientific Center Technical Note, TN 82.01.Google Scholar
  10. [Jaeschke & Schek, 1982]
    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.Google Scholar
  11. [Kobayashi, 1980]
    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.Google Scholar
  12. [Lipski, 1979]
    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.Google Scholar
  13. [Lipski, 1981]
    Lipski, W. Jr., “On Databases with Incomplete Information”, Journal of ACM, Vol.28, No.1, Jan 1981, pp.41–70.Google Scholar
  14. [MacLeod, 1983]
    MacLeod, I. A., “A Model for Integrated Information Systems”, Proc. of the ACM International Conf. on VLDB, Florence, 1983.Google Scholar
  15. [Maier, 1983]
    Maier, D., The Theory of Relational Databases, Computer Science Press, Rockville, 1983.Google Scholar
  16. [Makinouchi, 1977]
    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.Google Scholar
  17. [Michalewicz & Yeo, 1987]
    Michalewicz, Z. and Yeo, A., “Sets in Relational Databases”, Proceedings of the Canadian Information Processing Society, Edmonton, November 1987, pp.237–245.Google Scholar
  18. [Michalewicz & Yeo, 1988]
    Michalewicz, Z. and Yeo, A., “Interpreting Sets in Relational Databases”, submitted to Int. Conference on Statistical and Scientific Databases, Rome, June 1988.Google Scholar
  19. [Osborn & Heaven, 1986]
    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.Google Scholar
  20. [Schek & Pistor, 1982]
    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.Google Scholar
  21. [Schek & Scholl, 1986]
    Schek, H.-J. and Scholl, M. H., “The Relational Model with Relation-Valued Attributes”, Inform. Systems, Vol. 11, No.2, 1986, pp. 137–147.Google Scholar
  22. [Sowa, 1984]
    sSowa, J. F., Conceptual Structures, Addison-Wesley, 1984.Google Scholar
  23. [Thomas, 1983]
    Thomas, S., A Non-First-Normal Form Relational Database Model, Ph.D. Dissertation, Vanderblit University, August 1983.Google Scholar
  24. [Ullman, 1982]
    Ullman, J.D., Principles of Database Systems, Computer Science Press, 2nd edition, 1982.Google Scholar
  25. [Vassiliou, 1979]
    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.Google Scholar
  26. [Yeo, 1987]
    Yeo, A., Sets in Relational Databases, MSc. Thesis, Department of Computer Science, Victoria University, Wellington, New Zealand, 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Zbigniew Michalewicz
    • 1
  • Lindsay J. Groves
    • 2
  1. 1.University of North CarolinaCharlotte
  2. 2.Victoria University of WellingtonWellingtonNew Zealand

Personalised recommendations