Database Normalization: 4th Normal Form

This article is intended to be read after the Boyce-Codd normal form article.

Let's look at the situation where redundancies can creep in even though a table is in Boyce-Codd normal form. Let's take the student / instructor / course example used in that article, but change one of the initial assumptions.

Assume that the following is true for the tables below:

• Each instructor takes only one course

• Each course can have one or more instructors

• Each student can have several instructors per course (this is different to the previous example)

• Each student can take one or more courses

Student Course Instructor data, with several instructors per course

More data anomalies

Student	Course	Instructor
Student	Course	Instructor
Conrad Pienaar	Biology	Nkosizana Asmal
Dingaan Fortune	Mathematics	Kader Dlamini
Gerrie Jantjies	Science	Helen Ginwala
Mark Thobela	Biology	Nkosizana Asmal
Conrad Pienaar	Science	Peter Leon
Alicia Ncita	Science	Peter Leon
Quinton Andrews	Mathematics	Kader Dlamini
Dingaan Fortune	Mathematics	Helen Ginwala

The data is the same as before, except that Helen Ginwala is teaching science to Gerrie Jantjies as well as mathematics to Dingaan Fortune, and Dingaan Fortune is being taught by both Helen Ginwala and Kader Dlamini for mathematics.

The only possible key is a combination of all three attributes, as shown below. No other combination will uniquely identify a particular record.

Three attributes as key

Student Course Instructor table
Student Course Instructor table
Student
Instructor
Course

But this still has some potentially anomalous behavior. The fact that Kader Dlamini teaches mathematics is still stored more than once, as is the fact that Dingaan Thobela takes mathematics. The real problem is that the table stores more than one kind of fact: that of student-to-course relationship, as well as that of a student-to-instructor relationship. You can avoid this, as always, by separating the data into two tables, as shown below:

Creating a table for the student to instructor relationship

Student Instructor table
Student Instructor table
Student
Instructor

Creating a table for the student to course relationship

Student Instructor table
Student Instructor table
Student
Course

This situation exists when you have multiple multivalued dependencies. A multivalued dependency exists between two attributes when, for each value of the first attribute, there are one or more associated values of the second attribute. For each value of student, there were many values of course. This is the first multivalued dependency. Then, for each value of student, there are one or more associated values of instructor. This is the second multivalued dependency.

Thus, a table is in 4th normal form if:

• it is in Boyce-Codd normal form

• it does not contain more than one multivalued dependency

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