FD & MVD Axioms Rules

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MVD0 Complementation Rule

Let X, Y, and Z be sets of attributes that union is � and Y � Z � X. Then X �� Y if and only if X �� Z.

MVD1 - Reflexivity Rule

If Y � X, then X �� Y

MVD2 - Augmentation Rule

If Z � W and X �� Y, then XW �� YZ

MVD3 - Transitivity Rule

If X �� Y and Y �� Z, then X �� Z - Y

The following rules follow from the above MVD rules.

MVD4 - Pseudotransitivity Rule

If X �� Y and YW �� Z, then XW �� Z - YW

MVD5 - Union Rule

If X �� Y and X �� Z, then X �� YZ

MVD6 - Decomposition Rule

If X �� Y and X �� Z, then X �� Y � Z, X �� Y - Z, and X �� Z - Y

The rules of transitivity, pseudotransitivity, and decomposition are more restricted than the corresponding Functional Dependency rules.

FD-MVD1

If X � Y, then X �� Y

FD-MVD2

If X �� Z and Y � Z', where Z' � Z and Y and Z are disjoint, then X � Z'

FD-MVD3

If X �� Y and XY � Z, then X � Z - Y

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