Fourth Normal Form

Synonyms

4NF

Definition

Let R(A₁,…, A_n) be a relation schema and Σ a set of functional and multivalued dependencies over R(A₁,…, A_n). Then (R, Σ) is said to be in fourth normal form (4NF) if for every nontrivial multivalued dependency X ↠ Y implied by Σ, it holds that X is a superkey for R.

Key Points

In order to avoid update anomalies in database schemas containing functional and multivalued dependencies, 4NF was introduced by Fagin in [2]. As for the case of BCNF, this normal form is defined in terms of the notion of superkey as shown above. For example, given a relation schema R(A, B, C) and a set of functional dependencies Σ = {A → B}, it does not hold that (R (A, B, C), Σ) is in 4NF since A ↠ B is a nontrivial multivalued dependency implied by Σ and A is not a superkey for R. Similarly, relation schema S(A, B, C) and set of multivalued dependencies Σ = {A ↠ C} is not in 4NF since A is not a superkey for S. On the other hand, relation schema T(A, B, C) and set of functional and...