Created on March 10, 2013, 4:24 p.m. by Hevok & updated by Hevok on May 2, 2013, 5:36 p.m.

The Normal Form is the canonical, standard form of a Formula. It is required to for Entailment of assumption from a Description Logics Knowledge Base.

For example a Class Inclusion is substituted where the left side is negated and the Class Inclusion is replaced by a Disjunction. A Negation outside the braces is put inside the braces with the help of the De Morgans Law which turns a Disjunction into a Conjunction. This results into the Negation Normal Form of the original Formula.

  • Example: P ⊑ (E⊓U)⊔¬(¬E⊓D)
  • In NNF: ¬P ⊔ (E⊓U)⊔(E⊓¬D)

C⊑D = ¬C⊔D

¬(C⊔D) = ¬C ⊓ ¬D

The transformation of a Formula in DL Syntax to its Negation Normal Form is straightforward

  • Example:

    (A ⊓ D) ⊑ (B ⊔ ¬C)

    ¬(A ⊓ D) ⊔ (B ⊔ ¬C)
    ¬A ⊔ ¬D ⊔ B ⊔ ¬C


Tags: logic, formula, canonical
Categories: Concept
Parent: Tableaux Algorithm for ALC

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