Synonyms
Definition
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(x 1,  … , x k ), where P is a k-ary relational symbol, and x 1 ,  …  , x k are variables, not necessarily distinct.
Then tgds are formulas of the form ∀x(φ(x) →  ∃ y ψ(x, y)), where
- 1.
φ(x) is a conjunction of atomic formulas, all with variables among the variables in x.
- 2.
Every variable in x appears in φ(x) (but not necessarily in ψ(x, y)).
- 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...
Recommended Reading
Beeri C, Vardi MY. A proof procedure for data dependencies. J ACM. 1984;31(4):718–41.
Fagin R. Multivalued dependencies and a new normal form for relational databases. ACM Trans Database Sys. 1977;2(3):262–78.
Fagin R. Horn clauses and database dependencies. J ACM. 1982;29(4):952–85.
Fagin R, Kolaitis PG, Miller RJ, Popa L. Data exchange: semantics and query answering. Theor Comput Sci. 2005:89–124.
Zaniolo C. Analysis and design of relational schemata for database systems. PhD dissertation, UCLA. 1976.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2017 Springer Science+Business Media LLC
About this entry
Cite this entry
Fagin, R. (2017). Tuple-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_1274-2
Download citation
DOI: https://doi.org/10.1007/978-1-4899-7993-3_1274-2
Received:
Accepted:
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4899-7993-3
Online ISBN: 978-1-4899-7993-3
eBook Packages: Springer Reference Computer SciencesReference Module Computer Science and Engineering