1. Higher Normal Forms By John Nicosia CS 157a Fall 2007

2. What I Will Talk About Define Multi-valued Dependency (MVD) MVD v. FD Armstrong's Axioms for MVD Quick Review of 1NF, 2NF, 3NF, BCNF Fourth Normal Form (4NF)

3. Multi-valued Dependency (MVD) The multivalued dependency X --> --> Y holds in a relation R if whenever we have two tuples of R that agree in all the attributes of X, then we can swap their Y components and get two new tuples that are also in R. Trivial: If Y is a subset of X or X U Y is all the attributes of R. Non-Trivial: If Y is not a subset of X and X U Y is not all the attributes of R.

4. MVD v. FD

5. MVD v. FD (cont) Functional Dependency: 1. Every FD is a MVD. 2. FDs rule out certain tuples * If X --> Y then we can't have two tuples with the same X values but different Y values.

6. MVD v. FD (cont) Multi-Valued Dependency: 1. Not every MVD is a FD. 2. MVDs guarantee certain tuples exist. *If Name--> --> PhoneNum

7. How To Test for MVD

8. How To Test for MVD (cont)

12. Armstrong's Axioms for MVD Reflexivity Rule: if, then A -->-->B Complementation Rule: if A-->-->B, then A -->--> [R - ( )] Augmentation Rule: if A-->--> B and then (A,D) -->--> (B,C) Transitivity Rule: if A-->-->B and B-->-->C then A-->-->(C-B) Replication Rule: if A-->B then A-->--->B Coalescence Rule: if A-->-->B, (B, D) are disjoint, D--> C, then A-->C

13. Quick Review of Normal Forms 1NF: All values of the attributes contain no repeating values. 2NF: 1NF and every non-key attribute is fully dependent upon the primary key. 3NF: 2NF and every non-key attribute is functionally dependent only upon the primary key. BCNF: 3NF and every determinant (an attribute which some other attribute is fully functionally dependent) is a candidate key.

14. Fourth Normal Form (4NF) Fourth Normal Form (4NF): A relation schema R is in 4NF if there are no non- trivial multi-valued dependencies in R, or the determinant of any non-trivial multi- valued dependency in R is a super key of R. (Informal Definition)

15. 4NF Example

16. 4NF Example (cont)

20. Refrences http://en.wikipedia.org/wiki/Fourth_normal_f ormhttp://en.wikipedia.org/wiki/Fourth_normal_f orm Data Modeling and Database Design By Narayan S. Umanath and Richard W. Scamell