Armstrong’s Axioms

Infer functional dependencies from other functional dependencies

Note

Sound: Anything derived from $F$ is in $F^{+}$
Complete: Anything in $F^{+}$ can be derived

Reflexivity: If $Y \subseteq X$ holds then $X \to Y$ holds
Augmentation: If $X \to Y$ holds then $X Z \to Y Z$ holds
Transitivity: If $X \to Y$ and $Y \to Z$ holds then $X \to Z$ holds

Additional rules

Union: If $X \to Y$ and $X \to Z$ holds then $X \to Y Z$ holds
Decomposition: If $X \to Y Z$ holds then $X \to Y$ holds

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Functional Dependencies