Visualisation par l`exemple des dépendances dans les

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R
X→A X ⊆R A ∈R
X→A r r |=X→A
∀ti, tj∈r, ti[X] = tj[X]⇒ti[A] = tj[A]Fr
r Fd
F R f R
F F |=f∀r R r |=F r |=X→A
X F X+
F=
{A∈R|F|=X→A}R
P(R)R CL(F)
F F GEN(F)
CL(F)
titjr R X ⊆R
ag(ti, tj)ag(ti, tj) = {A∈R|ti[A] = tj[A]}
r ag(r)ag(r) = {ag(ti, tj)|ti, tj∈
r, ti6=tj}
R={R1, ..., Rn}Ri[X]⊆Rj[Y]Ri, Rj∈X
Y RiRjX Y
Ri[X]⊆Rj[Y]
={r1, ..., rn} |=Ri[X]⊆Rj[Y]
∀t∈ri,∃s∈rjt[X] = s[Y]πX(ri)⊆πY(rj)
I
I m (m≥1)
R1[X1]⊆R2[Y2]R2[X2]⊆R3[Y3]Rm[Xm]⊆R1[Y1]X1=Y1I
I Ri[X]⊆Rj[Y]
I I |=Ri[X]⊆Rj[Y]|=I
|=Ri[X]⊆Rj[Y]I J I J
I+=J+I+={Ri[X]⊆Rj[Y]I|=Ri[X]⊆Rj[Y}

I
Bd+(I)
IBd−(I)
I
R={R1, ..., Rn}F I
R d ={r1, ..., rn}R
F∪I α
|=α⇐⇒ F∪I|=α
r F
R r F
GEN (F)⊆ag(r)⊆CL(F)
F∪I

remakes
F={A−→ B, B −→ AC, CE −→ B, DE −→ C, AE −→ D, AD −→ E}
F
remakes
remakes
A(ID)