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.

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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