Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Database Dependencies

  • Marc Gyssens
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_1236

Synonyms

Database constraints; Data dependency

Definition

For a relational database to be valid, it is not sufficient that the various tables of which it is composed conform to the database schema. In addition, the instance must also conform to the intended meaning of the database [ 19]. While many aspects of this intended meaning are inherently informal, it will generally induce certain formalizable relationships between the data in the database, in the sense that whenever a certain pattern is present among the data, this pattern can either be extended or certain data values must be equal. Such a relationship is called a database dependency. The vast majority of database dependencies in the literature are of the following form [ 6]:
$$ \begin{array}{ll}&{}\left(\forall {x}_1\right)\dots \left(\forall {x}_n\right)\varphi \left({x}_1,\dots, {x}_n\right)\\ &{}\Rightarrow \left(\exists {z}_1\right)\dots \left(\exists {z}_k\right)\psi \left({y}_1,\dots, {y}_m,{z}_1,\dots,...
This is a preview of subscription content, log in to check access.

Recommended Reading

  1. 1.
    Abiteboul S,\enlargethispage*{1pc} Hull R, Vianu V. Foundations of databases. Reading: Addison-Wesley; 1995, (Part C).Google Scholar
  2. 2.
    Akhtar W, Cortés-Calabuig A, Paredaens J. Constraints in RDF. In: Semantics in data and knowledge bases, Lecture notes in computer science, vol. 6834. Berlin: Springer; 2011. p. 23–39.CrossRefzbMATHGoogle Scholar
  3. 3.
    Armstrong WW. Dependency structures of data base relationships. In: Proceedings of the IFIP Congress, Information Processing 74; 1974. p. 580–3.Google Scholar
  4. 4.
    Beeri C, Fagin R, Howard JH. A complete axiomatization for functional and multivalued dependencies. In: Proceedings of the ACM SIGMOD International Conference on Management of Data; 1978, p. 47–61.Google Scholar
  5. 5.
    Beeri C, Fagin R, Maier D, Yannakakis M. On the desirability of acyclic database schemes. J ACM. 1983;30(3):479–513.CrossRefMathSciNetzbMATHGoogle Scholar
  6. 6.
    Beeri C, Vardi MY. The implication problem for data dependencies. In: Proceedings of the International Conference on Algorithms, Languages, and Programming; 1981. Springer. p. 73–85.Google Scholar
  7. 7.
    Casanova MA, Fagin R, Papadimitriou CH. Inclusion dependencies and their interaction with functional dependencies. J Comput Syst Sci. 1984;28(1):29–59.CrossRefMathSciNetzbMATHGoogle Scholar
  8. 8.
    Chandra AK, Vardi MY. The implication problem for functional and inclusion dependencies is undecidable. SIAM J Comput. 1985;14(3):671–7.CrossRefMathSciNetzbMATHGoogle Scholar
  9. 9.
    Codd EF. A relational model of data for large shared data banks. Commun ACM. 1970;13(6):377–87.CrossRefzbMATHGoogle Scholar
  10. 10.
    Cohen DA, Jeavons P, Gyssens M. A unified theory of structural tractability for constraint satisfaction problems. J Comput Syst Sci. 2008;74(5):721–43.CrossRefMathSciNetzbMATHGoogle Scholar
  11. 11.
    Fagin R. Multivalued dependencies and a new normal form for relational databases. ACM Trans Database Syst. 1977;2(3):262–78.CrossRefMathSciNetGoogle Scholar
  12. 12.
    Fagin R, Kolaitis PG, Miller RJ, Popa L. Data exchange: semantics and query answering. Theor Comput Sci. 2005;336(1):89–124.CrossRefMathSciNetzbMATHGoogle Scholar
  13. 13.
    Fan W, Siméon J. Integrity constraints for XML. J Comput Syst Sci. 2003;66(1):254–91.CrossRefMathSciNetzbMATHGoogle Scholar
  14. 14.
    Gottlob G, Miklós Z, Schwentick T. Generalized hypertree decompositions: NP-hardness and tractable variants. J ACM. 2009;56(6):30:1–30:32.CrossRefMathSciNetzbMATHGoogle Scholar
  15. 15.
    Gyssens M. On the complexity of join dependencies. Trans Database Syst. 1986;11(1):81–108.CrossRefMathSciNetzbMATHGoogle Scholar
  16. 16.
    Herrmann C. On the undecidability of implications between embedded multivalued dependencies. Inf Comput. 1995;122(2):221–35.CrossRefMathSciNetzbMATHGoogle Scholar
  17. 17.
    Herrmann C. Corrigendum to “On the undecidability of implications between embedded multivalued database dependencies” [Inform. and Comput. 122(1995) 221–235]. Inf Comput. 204(12):1847–51, 2006.Google Scholar
  18. 18.
    Kanellakis PC. Elements of relational database theory. In: Van Leeuwen J, editor. Handbook of theoretical computer science. Amsterdam: Elsevier; 1991.p. 1074–156.Google Scholar
  19. 19.
    Paredaens J, De Bra P, Gyssens M, Van Gucht D. The structure of the relational database model. In: Brauer W, Rozenberg G, Salomaa A, editors. EATCS monographs on theoretical computer science, vol. 17. Berlin: Springer; 1989.Google Scholar
  20. 20.
    Petrov SV. Finite axiomatization of languages for representation of system properties. Inf Sci. 47(3):339–72, 1989.Google Scholar
  21. 21.
    Rissanen J. Independent components of relations. ACM Trans Database Syst. 1977;2(4):317–25.CrossRefGoogle Scholar
  22. 22.
    Zaniolo C. Analysis and design of relational schemata for database systems. Ph.D. thesis, University of California at Los Angeles; 1976. Technical Report UCLA-Eng-7669.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Hasselt UniversityHasseltBelgium

Section editors and affiliations

  • Leonid Libkin
    • 1
  1. 1.School of InformaticsUniversity of EdinburghEdinburghUK