Boolean logic

Conjunctive normal form

Abbreviated CNF

A Boolean formula written as an and of clauses.

Definition

Conjunctive normal form

Conjunctive normal form (CNF) is a conjunction of clauses, where each clause is a disjunction of literals.

Most CDCL solvers operate on CNF. A lowering procedure can introduce fresh variables while preserving whether the original formula is satisfiable.

01

Example

(a or b) and (not a or c) is a CNF formula with two clauses.

02

Important distinction

Equivalent-looking rewrites must preserve satisfiability; a malformed conversion can change the answer before the solver begins.

After reading this article, you should be able to

  • Define CNF in the sense used on this site.
  • Recognize CNF and evaluate all of its clauses under an assignment.