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:
“An “unemployed” existence is a worse negation of life than death itself.”
—José Ortega Y Gasset (1883–1955)
“What strikes many twin researchers now is not how much identical twins are alike, but rather how different they are, given the same genetic makeup....Multiples don’t walk around in lockstep, talking in unison, thinking identical thoughts. The bond for normal twins, whether they are identical or fraternal, is based on how they, as individuals who are keenly aware of the differences between them, learn to relate to one another.”
—Pamela Patrick Novotny (20th century)
“Humility is often only the putting on of a submissiveness by which men hope to bring other people to submit to them; it is a more calculated sort of pride, which debases itself with a design of being exalted; and though this vice transform itself into a thousand several shapes, yet the disguise is never more effectual nor more capable of deceiving the world than when concealed under a form of humility.”
—François, Duc De La Rochefoucauld (1613–1680)