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A Fourth Normal Form for Uncertain Data

  • Ziheng Wei
  • Sebastian LinkEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11483)

Abstract

Relational database design addresses applications for data that is certain. Modern applications require the handling of uncertain data. Indeed, one dimension of big data is veracity. Ideally, the design of databases helps users quantify their trust in the data. For that purpose, we need to establish a design framework that handles responsibly any knowledge of an organization about the uncertainty in their data. Naturally, such knowledge helps us find database designs that process data more efficiently. In this paper, we apply possibility theory to introduce the class of possibilistic multivalued dependencies that are a significant source of data redundancy. Redundant data may occur with different degrees, derived from the different degrees of uncertainty in the data. We propose a family of fourth normal forms for uncertain data. We justify our proposal showing that its members characterize schemata that are free from any redundant data occurrences in any of their instances at the targeted level of uncertainty in the data. We show how to automatically transform any schema into one that satisfies our proposal, without loss of any information. Our results are founded on axiomatic and algorithmic solutions to the implication problem of possibilistic functional and multivalued dependencies which we also establish.

Keywords

Database design Functional dependency Multivalued dependency Normal form Redundancy Uncertainty 

References

  1. 1.
    Chaudhry, N.A., Moyne, J.R., Rundensteiner, E.A.: An extended database design methodology for uncertain data management. Inf. Sci. 121(1–2), 83–112 (1999)CrossRefGoogle Scholar
  2. 2.
    Dubois, D., Prade, H.: Possibility theory. In: Meyers, R.A. (ed.) Computational Complexity: Theory, Techniques, and Applications, pp. 2240–2252. Springer, New York (2012).  https://doi.org/10.1007/978-1-4614-1800-9_139CrossRefGoogle Scholar
  3. 3.
    Fagin, R.: Multivalued dependencies and a new normal form for relational databases. ACM Trans. Database Syst. 2(3), 262–278 (1977)CrossRefGoogle Scholar
  4. 4.
    Galil, Z.: An almost linear-time algorithm for computing a dependency basis in a relational database. J. ACM 29(1), 96–102 (1982)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Hartmann, S., Link, S.: On a problem of Fagin concerning multivalued dependencies in relational databases. Theor. Comput. Sci. 353(1–3), 53–62 (2006)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Köhler, H., Link, S.: Inclusion dependencies and their interaction with functional dependencies in SQL. J. Comput. Syst. Sci. 85, 104–131 (2017)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Levene, M., Vincent, M.W.: Justification for inclusion dependency normal form. IEEE Trans. Knowl. Data Eng. 12(2), 281–291 (2000)CrossRefGoogle Scholar
  8. 8.
    Link, S.: Charting the completeness frontier of inference systems for multivalued dependencies. Acta Inf. 45(7–8), 565–591 (2008)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Link, S.: On the implication of multivalued dependencies in partial database relations. Int. J. Found. Comput. Sci. 19(3), 691–715 (2008)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Link, S.: Characterisations of multivalued dependency implication over undetermined universes. J. Comput. Syst. Sci. 78(4), 1026–1044 (2012)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Link, S., Prade, H.: Possibilistic functional dependencies and their relationship to possibility theory. IEEE Trans. Fuzzy Syst. 24(3), 757–763 (2016)CrossRefGoogle Scholar
  12. 12.
    Link, S., Prade, H.: Relational database schema design for uncertain data. In: Mukhopadhyay, S., et al. (eds.) Proceedings of the 25th ACM International Conference on Information and Knowledge Management, CIKM 2016, Indianapolis, IN, USA, 24–28 October 2016, pp. 1211–1220. ACM (2016)Google Scholar
  13. 13.
    Raju, K., Majumdar, A.K.: Fuzzy functional dependencies and lossless join decomposition of fuzzy relational database systems. ACM Trans. Database Syst. 13(2), 129–166 (1988)CrossRefGoogle Scholar
  14. 14.
    Sarma, A.D., Ullman, J.D., Widom, J.: Schema design for uncertain databases. In: Arenas, M., Bertossi, L.E. (eds.) Proceedings of the 3rd Alberto Mendelzon International Workshop on Foundations of Data Management, Arequipa, Peru, 12–15 May 2009, CEUR Workshop Proceedings, vol. 450 (2009)Google Scholar
  15. 15.
    Vincent, M.W.: Semantic foundations of 4NF in relational database design. Acta Inf. 36(3), 173–213 (1999)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Wei, Z., Link, S.: A fourth normal form for possibilistic data. Technical report 533, The University of Auckland, CDMTCS (2019)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Computer ScienceThe University of AucklandAucklandNew Zealand

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