Complete inference rules: FD: non-trivial RHS is Single attr + non subset of LHS proof: general and complete disproof: one negative example is enough Redefine key: set of attr functionally determine All other attrs and is “minimal” (no subset of key will be also key) primary/super-/sub-key binary relation: key? 1-1,1-m,m-m Closure operator +: fundamental operator Key: whose closure is all attr, and it is minimal utility: check given FD and 3NF why it works? Math. Proof. By induction prove closure is a fixed point (try by yourself first, to be briefed next lecture)

Closure Utility: check given FD diff forms of math induction: correct FD 1. no false positives: A1..An->B 2. no false negatives FD’s augmentation (LHS) not RHS Exercise: page 100. 3.5.1/2/4 Data mining/Knowledge discovery from data(KDD): rule discovery-statistical support FD discovery: find supporting for every tentative FD