We have seen in previous examples that propositions and the corresponding Boolean functions, in general, do not establish a one-to-one relationship. We want to find a syntactic form which establishes a one-to-one relationship with the corresponding Boolean function.
Let a $\phi$ be a proposition with a given syntactic form and let $f_\phi$ be corresponding Boolean function. We call a syntax $\operatorname{cnf}(\phi)$ which establishes a one-to-one relationship with $f_\phi$ a canonical normal form of $\phi$.
