\begin{frame} \frametitle{Natural Deduction} \begin{goal}{} \vspace{-1.5ex} \begin{align*} \alpha_1,\ldots,\alpha_n \;\vdash \; \beta \end{align*} means: there exists a \emph{natural deduction derivation} with \begin{itemize} \item premises $\alpha_1,\ldots,\alpha_n$, and \item conclusion $\beta$. \end{itemize} \end{goal} \pause\bigskip \begin{alertgoal}{} Natural deduction is a \emph{formal system} with \emph{strict formal rules}! \end{alertgoal} \end{frame}