Propositional logic formulas consist of \emph{atomic propositions}, \emph{logical operators}, and \emph{parentheses}.

The \emph{well-formed formulas} of propositional logic are those
which we obtain by using the construction rules below:
$$\varphi \coloneqq ~ < \text{atomic proposition>} ~ | ~\varphi \wedge \varphi~ |~ \varphi \vee \varphi~ | ~\neg \varphi ~| ~\varphi \imp \varphi~ | ~\varphi \leftrightarrow \varphi~ | ~( \varphi )$$