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)
“Perhaps the feelings that we experience when we are in love represent a normal state. Being in love shows a person who he should be.”
—Anton Pavlovich Chekhov (1860–1904)
“The old idea that the joke was not good enough for the company has been superseded by the new aristocratic idea that the company was not worthy of the joke. They have introduced an almost insane individualism into that one form of intercourse which is specially and uproariously communal. They have made even levities into secrets. They have made laughter lonelier than tears.”
—Gilbert Keith Chesterton (1874–1936)