Reasoning About FDs
Given some FDs, we can usually infer additional FDs:
- ssn did, did lot implies ssn lot
An FD f is implied by a set of FDs F if f holds whenever all FDs in F hold.
- = closure of F is the set of all FDs that are implied by F.
Armstrong’s Axioms (X, Y, Z are sets of attributes):
- Reflexivity: If Y X, then X Y
- Augmentation: If X Y, then XZ YZ for any Z
- Transitivity: If X Y and Y Z, then X Z
These are sound and complete inference rules for FDs!