Negation normal form is an elementary canonical form in mathematical logic. There are similar requirements for negation normal form in different logic fragments.
In predicate logic, a logical formula is in negation normal form if negation occurs only immediately above elementary propositions, and {} are the only allowed Boolean connectives. In classical logic each formula can be brought into this form by replacing implications and equivalences by their definitions, using De Morgan's laws to push negation inside, and eliminating double negations. This process can be represented using the following rewrite rules:
A formula in negation normal form can be put into the stronger conjunctive normal form or disjunctive normal form by applying the distributivity laws.
Famous quotes containing the words negation, normal and/or form:
“We make a mistake forsaking England and moving out into the periphery of life. After all, Taormina, Ceylon, Africa, America—as far as we go, they are only the negation of what we ourselves stand for and are: and we’re rather like Jonahs running away from the place we belong.”
—D.H. (David Herbert)
“Nothing is poetical if plain daylight is not poetical; and no monster should amaze us if the normal man does not amaze.”
—Gilbert Keith Chesterton (1874–1936)
“Touch me not.”
—Bible: New Testament Jesus, in John, 20:17.
Spoken to Mary Magdalene, after Jesus has risen from the dead and made himself known to her. The words are best known in the Latin form in which they appear in the Vulgate: Noli me tangere.