Encyclopedia of Database Systems

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

Third Normal Form

  • Marcelo ArenasEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_1264




Let R(A1,…, An) be a relation schema and Σ a set of functional dependencies over R(A1,…, An). An attribute Ai (i ∈{1,…,n}) is a prime attribute if Ai is an element of some key of R(A1,…, An). Then specification (R, Σ) is said to be in third normal form (3NF) if for every nontrivial functional dependency XA implied by Σ, it holds that X is a superkey for R or A is a prime attribute [1].

Key Points

In order to avoid update anomalies in database schemas containing functional dependencies, 3NF was introduced by Codd in [1]. This normal form is defined in terms of the notions of prime attribute and key as shown above. For example, given a relation schema R(A, B, C) and a set of functional dependencies Σ = {ABC, CB}, it holds that (R(A, B, C), Σ) is in 3NF since AB is a superkey and C is a prime attribute (given that AC is a key for R). On the other hand, (S(A, B, C), Γ) is not in 3NF if Γ = {AB}, since A is not a superkey for S and Bis not a prime...

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Recommended Reading

  1. 1.
    Codd EF. Further normalization of the data base relational model. In: Proceedings of data base systems. Englewood Cliffs: Prentice-Hall; 1972. p. 33–64.Google Scholar
  2. 2.
    Biskup J, Dayal U, Bernstein P. Synthesizing independent database schemas. In: Proceedings of the ACM SIGMOD International Conference on Management of Data; 1979. p. 143–51.Google Scholar
  3. 3.
    Jou J, Fischer P. The complexity of recognizing 3NF relation schemes. Inf Process Lett. 1982;14(4):187–90.zbMATHCrossRefGoogle 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