Rules of Functional Dependencies

Armstrong’s axioms

Armstrong’s axioms are a set of inference rules used to infer all the functional dependencies on a relational database. They were developed by William W. Armstrong in 1974.

We will denote a set of attributes by the letters X, Y, and Z. Also, we will represent the union of two sets of attributes X and Y by XY instead of the usual X $\cup$ Y; this notation is rather standard in database theory when dealing with sets of attributes.

We will now highlight the three primary rules:

Axiom of reflexivity

This axiom says, if Y is a subset of X, then X determines Y.

If Y $\subseteq$ X then , X $\rightarrow$ ...