\begin{frame}[t]{\sentence{Some Logicians} \; versus \; \sentence{All Logicians}}
  Recapitulating:
  \begin{talign}
    \mpause[1]{\formula{\forallst{x}{(\logimp{\unpred{L}{x}}{\unpred{C}{x}})}}} & & &
    \mpause{\sentence{\textit{all} logicians are clever}}
    \\
    \mpause{\formula{\existsst{x}{(\logand{\unpred{L}{x}}{\unpred{C}{x}})}}} & & &
    \mpause{\sentence{\textit{some} logicians are clever}} 
  \end{talign}
  \updatepause\vspace{-2ex}
  
  \begin{block}{\alert{Note:} 
    $\formula{\forallst{x}{(\logand{\unpred{L}{x}}{\unpred{C}{x}})}}$
    means something quite \alert{different}
  }
    \begin{itemize}\vspace{0.5ex}\setlength{\itemsep}{0.5ex}
    \pause
      \item for all \black{$x$}, \black{$x$} is a logician, and \black{$x$} is clever
    \pause
      \item every \black{$x$} is logician and clever
    \pause
      \item everybody is logician and clever
    \end{itemize}
  \end{block}
  \pause\medskip

  \begin{alertblock}{}
    What does $\formula{\existsst{x}{(\logimp{\unpred{L}{x}}{\unpred{C}{x}})}}$ mean?
    \alert{Hint: again very different.}
  \end{alertblock}
  \pause\medskip

  \begin{exampleblock}{Exercise}
    Specify a model such that:
    \begin{talign}
      \formula{\forallst{x}{(\logimp{\unpred{L}{x}}{\unpred{C}{x}})}}
      \lognotequiv
      \formula{\forallst{x}{(\logand{\unpred{L}{x}}{\unpred{C}{x}})}}  
    \end{talign}
  \end{exampleblock}
\end{frame}