Conjunctive Normal Form

A statement is in conjunctive normal form if it is a conjunction (sequence of ANDs) consisting of one or more conjuncts, each of which is a disjunction (OR) of one or more literals (i.e., statement letters and negations of statement letters; Mendelson 1997, p. 30). Examples of conjunctive normal forms include

(1)

(A v B) ^ (!A v C)

(2)

A v B

(3)

A ^ (B v C),

(4)

where v denotes OR, ^ denotes AND, and ! denotes NOT (Mendelson 1997, p. 30).

Every statement in logic consisting of a combination of multiple ^ , v , and !s can be written in conjunctive normal form.

An expression can be put in conjunctive normal form using the Wolfram Language using the following code:

 ConjunctiveNormalForm[f_] :=
 Not[LogicalExpand[Not[f]]] //. {
 Not[a_Or] :> And @@ (Not /@ List @@ a),
 Not[a_And] :> Or @@ (Not /@ List @@ a)
 }

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Mendelson, E. Introduction to Mathematical Logic, 4th ed. London: Chapman & Hall, p. 30, 1997.