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\begin{frame}
  \frametitle{Logical Reasoning}
  
  \begin{goal}{}
    \emph{From} $\alpha_1,\ldots,\alpha_n$ \emph{follows} $\beta$.
    \medskip
    
    This is denoted as:
    \begin{talign}
      \alpha_1,\ldots,\alpha_n \;\therefore\; \beta
    \end{talign}
  \end{goal}
  \pause
  
  \begin{exampleblock}{}
    \vspace{-1ex}
    \begin{tgather}
      p \wedge \neg q \;\therefore\; \neg q\\[.5ex]
      \mpause[1] { p \to (q \to r), \; p, \; \neg r \;\therefore\;} \mpause{ \neg q }
    \end{tgather}
  \end{exampleblock}
  \pause\pause\pause
  \bigskip
  
  \begin{goal}{Two Important Variants}
    \vspace{-1ex}
    \begin{talign}
      \text{semantic} & 
      \quad\quad \alpha_1,\ldots,\alpha_n \;\models \; \beta \\
      \text{syntactic} & 
      \quad\quad \alpha_1,\ldots,\alpha_n \;\vdash \; \beta 
    \end{talign}
  \end{goal}
\end{frame}