Negation

Negation is a logical operation that reverses a proposition’s truth value: it is true when the proposition is false and false when it is true.

Truth Table: A table that lists a logical expression’s truth value for every assignment of its variables. Its two-row pattern gives negation’s complete behavior for a single proposition.
Proposition: A declarative statement that is true or false. Negation takes a proposition as its input.
Negation as Failure: A nonmonotonic reasoning principle that treats inability to prove a claim as support for its negation. Unlike classical negation, it can express lack of proof rather than falsity.
Negation Normal Form: A formula form in which negation applies only to atomic propositions, with conjunctions and disjunctions as the other connectives. It reorganizes formulas by pushing negations inward using equivalence laws.
Logical Operator: A symbol or operation that combines or modifies propositions to form logical expressions. Negation is the simplest unary logical operator.
Truth Value: The value assigned to a proposition to indicate whether it is true or false. Negation reverses the input proposition’s truth value.
Intuitionistic Logic: A logic that interprets proofs constructively and does not accept every classical inference principle. Its negation does not generally make double negation equivalent to the original proposition.
Complement Gate: A digital logic circuit that outputs the inverse of a binary input. It implements propositional negation on a single digital signal.
Double Negation: The application of negation twice to a proposition, yielding an equivalent proposition in classical logic. It shows how two truth-value reversals cancel in classical logic.
Boolean Algebra: An algebraic system whose variables take truth-like values and whose operations include conjunction, disjunction, and complementation. Its complement operation gives an algebraic account of negation.

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