Conjunctive Normal Form

Conjunctive Normal Form

In Boolean logic, a formula is in conjunctive normal form (CNF) 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. It is similar to the product of sums form used in circuit theory.

All conjunctions of literals and all disjunctions of literals are in CNF, as they can be seen as conjunctions of one-literal clauses and conjunctions of a single clause, respectively. As in the disjunctive normal form (DNF), the only propositional connectives a formula in CNF can contain are and, or, and not. The not operator can only be used as part of a literal, which means that it can only precede a propositional variable.