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
