Double negation is a rule of inference and rule of replacement for classical propositional logic. It states that the negation of a negation of a proposition is logically equivalent to the affirmation of that proposition. ^{[1]}^{[2]} It is often expressed symbolically as so:

or even

.

Where means "replaceable".

In standard rule form, this rule may be represented as two subrules:

Please note it is not universally accepted. Some formulations of propositional logic omit this rule of inference (such as intuitionistic propositional logic).

**Rules of inference**

Modus Ponens | Modus Tollens | Disjunctive Syllogism | Hypothetical Syllogism | Conjunction Introduction | Conjunction Elimination | Disjunction Introduction | Disjunction Elimination | Bicondional Introduction | Biconditional Elimination | Constructive Dilemma | Destructive Dilemma | Absorption | Modus ponendo tollens

**Rules of Transformation**

**Double Negation** | Associative property | Commutative property | Distributive property | DeMorgan's Laws | Tautology | Exportation | Material Implication | Transposition

## ReferencesEdit

- ↑
*Double negation rule*. Retrevied January 27, 2017 from http://www.philosophy-index.com/logic/forms/double-negation.php. - ↑
*Double Negation*. Retrieved January 27 2017 from http://lc.brooklyn.cuny.edu/smarttutor/logic/dubneg.html.