What is Armstrong inference rules?

Answer 1

Armstrong's Inference Rules

• Specify rules for reasoning about dependency functions:
  • Reflexive rule:
    {Y 1,...,Y n}⊆{X1,...,Xm}
    implies {X1,...,Xm}→{Y 1,...,Y n} {Name,Sex}→{Name}
    
  • Augmentation Rule:
    {X1,...,Xm}→{Y 1,...,Y n}
    implies {X1,...,Xm,Z}→{Y 1,...,Y n,Z} {Name,Sex}→{Name}
    implies {Name,Sex,Age}→{Name,Age}
    
  • Transitive rule:
    {X1,...,Xm}→{Y 1,...,Y n},
    {Y 1,...,Y n}→{Z1,...,Zs}
    imply {X1,...,Xm}→{Z1,...,Zs} {Number}→{Name}
    {Name}→{Sex}
    imply{Number}→{Sex}
    
• Armstrong inference rules are sound Produce only functional dependencies belonging to the closure complete Produce all the functional dependencies in the closure