A tuple-generating dependency (tgd) (Been and Vardi [1984], Fagin [1982],
Yannakakis and Papadimitriou [1982]) is a formula of the form
VJC
3y [ψ
1
(JC
)
-^ψ
2
(x , y )], where χ and y are vectors of variables and both ψ
1
and ψ
2
are
conjunctions of atoms. We write a tgd without the quantifiers, e.g.,
G(y,z)
—
G(y,w)
Λ C(u>) instead of Vy Vz 3w
[G(y,z)
—
G(y,w)
Λ C(w>)]. Univer-
sally quantified variables are those appearing in the left-hand side of the for-
mula (these variables can also appear in the right-hand side). Existentially
quantified variables are those appearing only in the right-hand side of th ...
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