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:
“Michelangelo said to Pope Julius II, “Self negation is noble, self-culture is beneficent, self-possession is manly, but to the truly great and inspiring soul they are poor and tame compared to self-abuse.” Mr. Brown, here, in one of his latest and most graceful poems refers to it in an eloquent line which is destined to live to the end of time—”None know it but to love it, None name it but to praise.””
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)
“Literature is a defense against the attacks of life. It says to life: “You can’t deceive me. I know your habits, foresee and enjoy watching all your reactions, and steal your secret by involving you in cunning obstructions that halt your normal flow.””
—Cesare Pavese (1908–1950)
“As for the terms good and bad, they indicate no positive quality in things regarded in themselves, but are merely modes of thinking, or notions which we form from the comparison of things with one another. Thus one and the same thing can be at the same time good, bad, and indifferent. For instance music is good for him that is melancholy, bad for him who mourns; for him who is deaf, it is neither good nor bad.”
—Baruch (Benedict)