Definition:Conjunctive Normal Form

Definition
A propositional formula $P$ is in conjunctive normal form (CNF for short) if it consists of a conjunction of:
 * $(1):\quad$ disjunctions of literals

and/or:
 * $(2):\quad$ literals.

Examples

 * $\left({\neg p \lor q \lor r}\right) \land \left({\neg q \lor r}\right) \land \left({\neg r}\right)$

is in CNF.


 * $\left({\neg p \lor q \lor r}\right) \land \left({\left({p \land \neg q}\right) \lor r}\right) \land \left({\neg r}\right)$

is not in CNF because there is a conjunction buried in the second disjunction.


 * $\left({\neg p \lor q \lor r}\right) \land \neg \left({\neg q \lor r}\right) \land \left({\neg r}\right)$

is not in CNF because the second disjunction is negated.


 * $p \land q$

is in CNF, as it is a conjunction of literals.


 * $p \lor q$

is in CNF, as it is a trivial (one-element) conjunction of a disjunction of literals.

Also known as
This is often found referred to in its abbreviated form CNF.

Also see

 * Disjunctive Normal Form (DNF)
 * Negation Normal Form (NNF)