Relational Database Question:
Explain Armstrong rules? How they are complete and/or sound?
Answer:
The well-known inference rules for FDs
►► Reflexive rule :
If Y is subset or equal to X then X Y.
►► Augmentation rule:
If X Y then XZ YZ.
►► Transitive rule:
If {X Y, Y Z} then X Z.
►► Decomposition rule :
If X YZ then X Y.
►► Union or Additive rule:
If {X Y, X Z} then X YZ.
►► Pseudo Transitive rule :
If {X Y, WY Z} then WX Z.
Of these the first three are known as Amstrong Rules. They are sound because it is enough if a set of FDs satisfy these three. They are called complete because using these three rules we can generate the rest all inference rules.
►► Reflexive rule :
If Y is subset or equal to X then X Y.
►► Augmentation rule:
If X Y then XZ YZ.
►► Transitive rule:
If {X Y, Y Z} then X Z.
►► Decomposition rule :
If X YZ then X Y.
►► Union or Additive rule:
If {X Y, X Z} then X YZ.
►► Pseudo Transitive rule :
If {X Y, WY Z} then WX Z.
Of these the first three are known as Amstrong Rules. They are sound because it is enough if a set of FDs satisfy these three. They are called complete because using these three rules we can generate the rest all inference rules.
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