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Conjunctive Normal Form (CNF)

Definition - What does Conjunctive Normal Form (CNF) mean?

Conjunctive normal form (CNF) is an approach to Boolean logic that expresses formulas as conjunctions of clauses with an AND or OR. Each clause connected by a conjunction, or AND, must be either a literal or contain a disjunction, or OR operator. CNF is useful for automated theorem proving.

Techopedia explains Conjunctive Normal Form (CNF)

In conjunctive normal form, statements in Boolean logic are conjunctions of clauses with clauses of disjunctions. In other words, a statement is a series of ORs connected by ANDs.

For example:

(A OR B) AND (C OR D)

(A OR B) AND (NOT C OR B)

The clauses may also be literals:

A OR B

A AND B

Literals are seen in CNF as conjunctions of literal clauses and conjunctions that happen to have a single clause. It is possible to convert statements into CNF that are written in another form, such as disjunctive normal form.

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