A formula of propositional logic is in conjunctive normal form or clausal normal form (CNF) if it is a conjunction of one or more clauses, where a clause is a disjunction of literals. It is also sometimes called product of sums and AND of ORs.

CNF enables a powerful resolution rule of inference, and this is widely used in automatic theorem proving and SAT solver.

Clause

A literals is either an atomic sentence or a negation of an atomic sentence:

A clause is a set of literals. For example:

A clause is interpreted as a disjunction of its elements. For example, is interpreted as .

Note that the empty set is also a clause. It is equivalent to an empty disjunction and, therefore, is unsatisfiable.

See Also

References