If F is set of functional dependencies then the closure of F, denoted as F+, is the set of all functional dependencies logically implied by F. Armstrong’s Axioms are set of rules, when applied repeatedly generates closure of functional dependencies.
- Reflexive rule: If alpha is a set of attributes and beta is_subset_of alpha, then alpha holds beta.
- Augmentation rule: if a → b holds and y is attribute set, then ay → by also holds. That is adding attributes in dependencies, does not change the basic dependencies.
- Transitivity rule: Same as transitive rule in algebra, if a → b holds and b → c holds then a → c also hold. a → b is called as a functionally determines b