Relational-Database-Design-Functional-Dependency

Functional dependencies are some constraints on the set of legal relations.
The constraint is that the value for a certain set of attributes uniquely determines the value for another set of attributes. 约束条件是一组属性的值唯一确定另一组属性的值
A functional dependency is a generalization of the notion of a key. 功能依赖关系是键概念的泛化

Functional Dependency Property 功能依赖

  • is a super key for relation schema iff

  • is a condidate key for iff and for no

  • Functional dependencies can express constraints that cannot be expressed using superkeys.
    For example:

We can use functional dependency to hold

But would not expect the following to hold:

  • we can use functional dependency to specify constraints on the set of legal relations

  • Trivial
    A functional dependency is trivial if it is satisfied by all instances of a relation.
    Equivalently,
    If is trivial.
    Example:

Closure of a Set of Functional Dependencies 功能依赖的闭包

The set of all functional dependencies logically implied by is the closure of , denoted by .

is a superset of .

How to find

  • Applying Armstrong's Axioms
    1. reflexivity
      • if then
    2. augumentation
      • if then for any .
    3. transitivity
      • if and , then
  • These rules are sound and complete.

This method is also apply in Attribute Closure.

Prove Armstrong's Axioms

For Union:
If then

  2. According to augmentation
  6. According to transitivity

For Decomposition:
if , then and

  2. according to reflexivity
  3. according to reflexivity
  4. according to transitivity

For pseudotransitivity
if and then

  2. according to augmentation
  3. according to transitivity
Table Of Contents
Relational-Database-Design-Functional-Dependency
Functional Dependency Property 功能依赖
Closure of a Set of Functional Dependencies 功能依赖的闭包
How to find
Prove Armstrong's Axioms