Relational Database Model

FD & MVD Axioms Rules

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.


If X Y, then X Y


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


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

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