Change - Normalform

Created on March 10, 2013, 4:24 p.m. by Hevok & updated on March 11, 2013, 8:12 p.m. by Hevok

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. ¶
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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. ¶
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Example: P ⊑ (E⊓U)⊔¬(¬E⊓D) ¶
In NNF: ¬P ⊔ (E⊓U)⊔(E⊓¬D) ¶
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C⊑D = ¬C⊔D ¶
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¬(C⊔D) = ¬C ⊓ ¬D ¶
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The transformation of a Formula in DL Syntax to its Negation Normal Form is straightforward ¶
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* Example: ¶
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(A ⊓ D) ⊑ (B ⊔ ¬C) ¶
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¬(A ⊓ D) ⊔ (B ⊔ ¬C)
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¬A ⊔ ¬D ⊔ B ⊔ ¬C