Armstrong's Axioms

relational-algebra

Definition

Armstrong's Axioms

Armstrong’s axioms are a set of axioms (or, more precisely, inference rules) used to infer all the functional dependencies.

Inference Rules

Reflexivity

Reflexivity

Let be a schema of a relation and (subsets of attributes of ).

If , then functionally determines :

Augmentation

Augmentation

Let be a schema of a relation and (subsets of attributes of ).

If functionally determines , then functionally determines .

Trivially, this is true since is a trivial functional dependency.

Transitivity

Transitivity

Let be a schema of a relation and (subsets of attributes of ).

If functionally determines and functionally determines , then functionally determines .

Further Inference Rules

Further inference rules can be derived from the base rules.

Composition

Composition

Let be a schema of a relation and (subsets of attributes of ).

If functionally determines and functionally determines , then functionally determines .

Decomposition

Decomposition

Let be a schema of a relation and (subsets of attributes of ).

If functionally determines , then functionally determines and functionally determines .

Pseudo Transitivity

Pseudo Transitivity

Let be a schema of a relation and (subsets of attributes of ).

If functionally determines and functionally determines , then functionally determines .