Conjunctive Normal Form

What Does Conjunctive Normal Form 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.

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Techopedia Explains Conjunctive Normal Form

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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Margaret is an award-winning technical writer and teacher known for her ability to explain complex technical subjects to a non-technical business audience. Over the past twenty years, her IT definitions have been published by Que in an encyclopedia of technology terms and cited in articles by the New York Times, Time Magazine, USA Today, ZDNet, PC Magazine, and Discovery Magazine. She joined Techopedia in 2011. Margaret's idea of a fun day is helping IT and business professionals learn to speak each other’s highly specialized languages.