Database Normalization: 4NF

Fourth Normal Form (4NF) is a level of database normalization designed to eliminate multi-valued dependencies, which are a more subtle type of redundancy not handled by 3NF or even Boyce-Codd Normal Form (BCNF).

🔄 Quick Recap of Earlier Forms

Normal Form	What It Solves
1NF	Atomicity (no repeating groups, each column has atomic values)
2NF	Partial dependencies (applies to composite keys)
3NF	Transitive dependencies (non-key depending on another non-key)
BCNF	Every determinant is a candidate key (a stricter form of 3NF)

🧩 What Is a Multi-Valued Dependency?

A multi-valued dependency (MVD) occurs when:

For a single value of attribute A, there are multiple independent values of attribute B and attribute C — and B and C are independent of each other.

This leads to repetition and redundancy if not separated.

📌 4NF Rule

A table is in 4NF if:

It is already in Boyce-Codd Normal Form (BCNF)
AND it has no non-trivial multi-valued dependencies

🧠 Example

Not in 4NF

StudentCoursesLanguages
-------------------------
Student | Course | Language
--------|--------|---------
Alice   | Math   | English
Alice   | Math   | French
Alice   | History| English
Alice   | History| French

Here:

Each student can take multiple courses
Each student can speak multiple languages
But Courses and Languages are independent!

This causes a multi-valued dependency: Student →→ Course and Student →→ Language

Split into 4NF

StudentCourses
---------------
Student | Course
--------|--------
Alice   | Math
Alice   | History

StudentLanguages
----------------
Student | Language
--------|----------
Alice   | English
Alice   | French

Now the redundancy is gone, and MVDs are eliminated ✅

🛠 Summary

Aspect	4NF
Based on	BCNF + No Multi-Valued Dependencies
Solves	Redundancy due to independent multivalued facts
Common Fix	Decompose into multiple relations
Real-World Usage	Often important in design of many-to-many relationships