\subsection{Propositional logic}
\subsubsection{Syntax}
\inlinedefinition For a set of variables $\cV$, the \bi{language of propositional logic} $\cL_P$ is the smallest set where
\begin{multicols}{2}
    \begin{itemize}
        \item $X \in \cL_P$ if $X \in \cV$
        \item $\bot \in \cL_P$
        \item $A \land B \in \cL_P$ if $A \in \cL_P$ and $B \in \cL_P$
        \item $A \lor B \in \cL_P$ if $A \in \cL_P$ and $B \in \cL_P$
        \item $A \rightarrow B \in \cL_P$ if $A \in \cL_P$ and $B \in \cL_P$
    \end{itemize}
\end{multicols}
