Inference Rules
There are 6 inference rules, which are defined below:
- Reflexive Rule: According to this rule, if B is a subset of A then A logically determines B. Formally, B ⊆ A then A → B.
- Example: Let us take an example of the Address (A) of a house, which contains so many parameters like House no, Street no, City etc. These all are the subsets of A. Thus, address (A) → House no. (B).
- Augmentation Rule: It is also known as Partial dependency. According to this rule, If A logically determines B, then adding any extra attribute doesn’t change the basic functional dependency.
- Example: A → B, then adding any extra attribute let say C will give AC → BC and doesn’t make any change.
- Transitive rule: Transitive rule states that if A determines B and B determines C, then it can be said that A indirectly determines B.
- Example: If A → B and B → C then A → C.
- Union Rule: Union rule states that If A determines B and C, then A determines BC.
- Example: If A → B and A → C then A → BC.
- Decomposition Rule: It is perfectly reverse of the above Union rule. According to this rule, If A determined BC then it can be decomposed as A → B and A → C.
- Example: If A → BC then A → B and A → C.
- Pseudo Transitive Rule: According to this rule, If A determined B and BC determines D then BC determines D.
- Example: If A → B and BC → D then AC → D.
Inference Rules in DBMS
Inference rules in databases are also known as Armstrong’s Axioms in Functional Dependency. These rules govern the functional dependencies in a relational database. From inference rules a new functional dependency can be derived using other FDs. These rules were introduced by William W. Armstrong. In this article, we will come to know about all the rules proposed by him. Also, we will be exploring the prerequisites for it and will understand the topic in a better way.
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