Relational Database Model

Armstrong's Axioms Rules

FD1 - Reflexivity Rule

If Y X, then X Y

FD2 - Augmentation Rule

If Z W and X Y, then XW YZ

FD3 - Transitivity Rule

If X Y and Y Z, then X Z

There are three additional rules that are implied by the above rules.

FD4 - Pseudotransitivity Rule

If X Y and YW Z, then XW Z

FD5 - Union Rule

If X Y and X Z, then X YZ

FD6 - Decomposition Rule

If X YZ, then X Y and X Z

The rules of union and decomposition imply that we can always replace a set of functional dependencies with an equivalent set that has only functional dependencies of the form X A (i.e., the right-hand side contains a single attribute).

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