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Equality-Generating Dependencies

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Encyclopedia of Database Systems

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Synonyms

egd

Definition

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(x 1,...,x k ), where P is a k-ary relational symbol and x 1,…,x k are variables, not necessarily distinct.

Then egds are formulas of the form ∀x(ϕ(x) → (x 1 = x 2)), where:

  • Ï•(x) is a conjunction of atomic formulas, all with variables among the variables in x.

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

  • x 1 and x 2 are distinct variables in x.

Conditions (1) and (2) together are sometimes replaced by the weaker condition that Ï•(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...\forall {x}_k\forall...

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Recommended Reading

  1. Beeri C, Vardi MY. A proof procedure for data dependencies. J ACM. 1984;31(4):718–41.

    Article  MathSciNet  MATH  Google Scholar 

  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. Fagin R. Horn clauses and database dependencies. J ACM. 1982;29(4):952–85.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. IBM Almaden Research Center, San Jose, CA, USA

    Ronald Fagin

Authors
  1. Ronald Fagin
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Correspondence to Ronald Fagin .

Editor information

Editors and Affiliations

  1. Georgia Institute of Technology College of Computing, Atlanta, Georgia, USA

    Ling Liu

  2. University of Waterloo School of Computer Science, Waterloo, Ontario, Canada

    M. Tamer Özsu

Section Editor information

  1. School of Informatics, University of Edinburgh, Crichton Street, EH8 9LE, Edinburgh, Scotland, UK

    Leonid Libkin

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Fagin, R. (2017). Equality-Generating Dependencies. In: Liu, L., Özsu, M. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4899-7993-3_1273-2

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  • DOI: https://doi.org/10.1007/978-1-4899-7993-3_1273-2

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4899-7993-3

  • Online ISBN: 978-1-4899-7993-3

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