Tuple-Generating Dependencies

Synonyms

Equality-generating dependency (egd)

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...