Encyclopedia of Database Systems

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

Fourth Normal Form

  • Marcelo ArenasEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_9002




Let R(A1,…, An) be a relation schema and Σ a set of functional and multivalued dependencies over R(A1,…, An). Then (R, Σ) is said to be in fourth normal form (4NF) if for every nontrivial multivalued dependency XY implied by Σ, it holds that X is a superkey for R.

Key Points

In order to avoid update anomalies in database schemas containing functional and multivalued dependencies, 4NF was introduced by Fagin in [2]. As for the case of BCNF, this normal form is defined in terms of the notion of superkey as shown above. For example, given a relation schema R(A, B, C) and a set of functional dependencies Σ = {A → B}, it does not hold that (R (A, B, C), Σ) is in 4NF since AB is a nontrivial multivalued dependency implied by Σ and A is not a superkey for R. Similarly, relation schema S(A, B, C) and set of multivalued dependencies Σ = {AC} is not in 4NF since A is not a superkey for S. On the other hand, relation schema T(A, B, C) and set of functional and...

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Recommended Reading

  1. 1.
    Beeri C. On the membership problem for functional and multivalued dependencies in relational databases. ACM Trans Database Syst. 1980;5(3):241–59.zbMATHCrossRefGoogle Scholar
  2. 2.
    Fagin R. Multivalued dependencies and a new normal form for relational databases. ACM Trans Database Syst. 1977;2(3):262–78.MathSciNetCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Pontifical Catholic University of ChileSantiagoChile

Section editors and affiliations

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