Conjunctive normal form

a.k.a.

• CNF

Define

… as every molecular statement written as a

\(\{ x_1, x_2, \ldots \}\) in the form

\[\begin{gather*}
  f
  =
  \underbrace{(\ell_{11} \lor \ell_{12} \lor \cdots)}_{\textstyle c_1}
  \land
  \underbrace{(\ell_{21} \lor \ell_{22} \lor \cdots)}_{\textstyle c_2}
  \land \cdots,
  \\[1ex]
  \text{with} \quad
  \forall (i, j), \> \quad \exists k
  \quad \text{such that} \quad
  \boxed{\ell_{ij} = x_k}
  \quad \text{or} \quad
  \boxed{\ell_{ij} = \lnot x_k},
\end{gather*}
\]