Encyclopedia of Database Systems

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

Equality-Generating Dependencies

  • Ronald FaginEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_1273




Equality-generating dependencies, or egds, are one of the two major types of database dependencies (the other major type consists of tuple-generating dependencies, or tgds).

To define egds, it is necessary to begin with the notion of an atomic formula, which is a formula of the form P(x1,…,xk), where P is a k-ary relational symbol and x1,…,xk are variables, not necessarily distinct.

Then egds are formulas of the form ∀ x(ϕ( x) → ( x 1 = x 2)), where:
  • ϕ(x) is a conjunction of atomic formulas, all with variables among the variables in x.

  • Every variable in x appears in ϕ(x).

  • x1 and x2 are distinct variables in x.

Conditions (1) and (2) together are sometimes replaced by the weaker condition that ϕ(x) be an arbitrary first-order formula with free variables exactly those in x.

Key Points

The most important example of an egd is a functional dependency, where an example is the formula
$$ \begin{array}{l}\forall {x}_1 \ldots \forall {x}_k\forall...
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Recommended Reading

  1. 1.
    Beeri C, Vardi MY. A proof procedure for data dependencies. J ACM. 1984;31(4):718–41.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Codd EF. Further normalization of the data base relational model. In: Database systems, Courant computer science series 6. Englewood Cliffs: Prentice-Hall; 1972. p. 33–64.Google Scholar
  3. 3.
    Fagin R. Horn clauses and database dependencies. J ACM. 1982;29(4):952–85.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.IBM Almaden Research CenterSan JoseUSA

Section editors and affiliations

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