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, 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).
x1 and x2 are distinct variables in x.
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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