Encyclopedia of Database Systems

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

Tuple-Generating Dependencies

  • Ronald FaginEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_1274




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

To define tgds, the notion of an atomic formula is first needed, 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 tgds are formulas of the form ∀ x( φ( x) → ∃ y ψ( x, y)), where
  1. 1.

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

  2. 2.

    Every variable in x appears in φ(x) (but not necessarily in ψ(x, y)).

  3. 3.

    ψ(x, y) is a conjunction of atomic formulas, all with variables among the variables in x and y.


If y is empty, so that there are no existentially quantified variables, then the tgd is called full.

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.

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Recommended Reading

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    Beeri C, Vardi MY. A proof procedure for data dependencies. J ACM. 1984;31(4):718–41.MathSciNetzbMATHCrossRefGoogle Scholar
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    Fagin R. Multivalued dependencies and a new normal form for relational databases. ACM Trans Database Sys. 1977;2(3):262–78.MathSciNetCrossRefGoogle Scholar
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    Fagin R. Horn clauses and database dependencies. J ACM. 1982;29(4):952–85.MathSciNetzbMATHCrossRefGoogle Scholar
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    Fagin R, Kolaitis PG, Miller RJ, Popa L. Data exchange: semantics and query answering. Theor Comput Sci. 2005;336(1):89–124.MathSciNetzbMATHCrossRefGoogle Scholar
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    Zaniolo C. Analysis and design of relational schemata for database systems. PhD dissertation, UCLA. 1976.Google 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