Armstrong's axioms
Armstrong's axioms are a set of axioms (or, more precisely, inference rules ) used to infer all the functional dependencies on a relational database . They were developed by William W. Armstrong in his 1974 paper. The axioms are sound in generating only functional dependencies in the closure of a set of functional dependencies (denoted as {\displaystyle F^{+}} ) when applied to that set (denoted as {\displaystyle F} ). They are also complete in that repeated application of these rules will generate all functional dependencies in the closure {\displaystyle F^{+}} . Axioms Let {\displaystyle R(U)} be a relation scheme over the set of attributes {\displaystyle U} . {\displaystyle X} , {\displaystyle Y} , {\displaystyle Z} denotes any subset of {\displaystyle U} and, for short, the union of two sets of attributes...