Synonyms
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, where an example is the formula 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
- 1.
Ï•(x) is a conjunction of atomic formulas, all with variables among the variables in x.
- 2.
Every variable in x appears in Ï•(x).
- 3.
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
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Recommended Reading
Beeri C. and Vardi M.Y. A proof procedure for data dependencies. J. ACM, 31(4):718–741, 1984.
Codd E.F. Further normalization of the data base relational model. Courant Computer Science Series 6: Database Systems. Prentice-Hall, USA, 1972, pp. 33–64.
Fagin R. Horn clauses and database dependencies. J. ACM, 29(4):952–985, 1982.
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Fagin, R. (2009). Equality-Generating Dependencies. In: LIU, L., ÖZSU, M.T. (eds) Encyclopedia of Database Systems. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-39940-9_1273
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