Inference Rule (IR)

• Using the inference rule, we can derive additional FD (functional dependency) from the initial attribute set.

Types Of Inference Rule

The FD (Functional dependency) has 6 types of inference rules. Any rule can be used in-between two attributes

1. Reflexive Rule (IR1)

• In the reflexive rule, if B is a subset of A, then A determines B.
• Every attribute can determine itself also called Reflexive.
• If A ⊇ B,, then A  →   B

Example:

A ⊇  A , B  →  B  , AB  →    B

2. Augmentation Rule (IR2)

• The augmentation rule is also called a partial dependency.
• If A    → B, then AC   →   BC   

3. Transitive Rule (IR3)

• In the transitive rule, if A determines B and B determines C, then A must also determine C.
• If A   →   B and B  →  C, then A  →   C    

4. Union Rule (IR4)

• Union rule says, that if A determines B and B determines C, then A must also determine B and C.
• If A  →  B and A   →  C, then A  →    BC     

5. Decomposition Rule (IR5)

• The decomposition rule is also called the project rule. It is the reverse of the union rule.
• If A → BC, then A → B and A →    C   

6. Pseudo transitive Rule (IR6)

According to this Rule

• If A   → B and BC   →   W, then AC   →   W