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.
φ(x) is a conjunction of atomic formulas, all with variables among the variables in x.
Every variable in x appears in φ(x) (but not necessarily in ψ(x, y)).
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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