Negation normal form
Encyclopedia
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 rule
s:
A formula in negation normal form can be put into the stronger conjunctive normal form
or disjunctive normal form
by applying the distributivity laws.
Negation
In logic and mathematics, negation, also called logical complement, is an operation on propositions, truth values, or semantic values more generally. Intuitively, the negation of a proposition is true when that proposition is false, and vice versa. In classical logic negation is normally identified...
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 ruleRewrite rule
In linguistics, a rewrite rule for natural language in generative grammar is a rule of the form A → X where A is a syntactic category label, such as noun phrase or sentence, and X is a sequence of such labels and/or morphemes, expressing the fact that A can be replaced by X in generating the...
s:
A formula in negation normal form can be put into the stronger conjunctive normal form
Conjunctive normal form
In Boolean logic, a formula is in conjunctive normal form if it is a conjunction of clauses, where a clause is a disjunction of literals.As a normal form, it is useful in automated theorem proving...
or disjunctive normal form
Disjunctive normal form
In boolean logic, a disjunctive normal form is a standardization of a logical formula which is a disjunction of conjunctive clauses. As a normal form, it is useful in automated theorem proving. A logical formula is considered to be in DNF if and only if it is a disjunction of one or more...
by applying the distributivity laws.