Armstrong’s Axioms in DBMS

Armstrong’s Axioms are a set of rules of axioms. It was developed by William W.Armstrong in 1974. It is used to infer all the functional dependencies on a relational database.

Primary Rule:

  • Reflexive Rule
  • Augmentation Rule
  • Transitive Rule
  • Reflexive Rule :

    If Y ⊆ X then X → Y if Y is a subset of attribute of X.

    Reflexive Rule :

    If X → Y then XZ → YZ for a pair of tuple t1 and t2.
    If t1[X] = t2[X] then it implies that
    ∴ t1[Y] = t2[Y]
    on the other hand,
    If t1[XZ] = t2[XZ] then it implies that
    ∴ t1[YZ] = t2[YZ] then
    ∴ t1[XZ] = t2[YZ]

    Transitive Rule :

    If X → Y and Y → Z
    then If X → Z

    Secondary Rule:

  • Decomposition Rule
  • Union Rule
  • Pseudo Transitive Rule
  • Decomposition Rule :

    If X → YZ
    then X → Y and X → Z

    Decomposition Rule :

    If X → Y and X → Z
    then X → YZ

    Pseudo Transitive Rule :

    If X → YZ and Y → W
    then X → WZ