Armstrong's axioms
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Armstrong's axioms are a set of axioms used to infer all the functional dependencies on a relational database. They were developed by William W. Armstrong on his paper Dependency Structures of Data Base Relationships published in 1974. The axioms are sound in that they generate only functional dependencies in the closure of a set of functional dependencies (denoted as F+) when applied to that set (denoted as F). They are also complete in that repeated application of these rules will generate all functional dependencies in the closure F+.
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[edit] Axioms
[edit] Axiom of reflexivity
If 
, then 
[edit] Axiom of augmentation
If , then 
for any Z
Where XZ means the collection of all attributes in X and Z.
[edit] Axiom of transitivity
If and 
, then 
[edit] Additional rules
[edit] Union
If and then 
[edit] Decomposition
If , then and
[edit] Pseudo Transitivity
If 
and 
then 
