\begin{frame}
  \frametitle{Examples}

  \begin{exampleblock}{}
    Examples of formulas
    \begin{itemize}
      \item $\neg\myall{x}{P(x)}$ 
        \mpause[2]{\\\hint{Not everybody is green.}}
      \item $\myex{x}{\neg P(x)}$ 
        \mpause{\\\hint{There exists someone who is not green.}}
      \item $\myall{x}{\neg R(x,x)}$
        \mpause{\\\hint{Everybody does not know himself.}}
      \item $\myall{x}{(R(x,x) \to \neg P(x))}$
        \mpause{\\\hint{Everybody, who knows himself, is not green.}}
      \item $\myall{x}{\myall{y}{(R(x,y) \to \neg R(y,x))}}$
        \mpause{\\\hint{For all $x$ and $y$, if $x$ knows $y$ then $y$ does not know $x$.}}
    \end{itemize}
  \end{exampleblock}
  \bigskip\pause
  
  What do these formulas mean given that
  \begin{itemize}
    \item $P(x)$ means `$x$ is green'
    \item $R(x,y)$ means `$x$ knows $y$'
  \end{itemize}
\end{frame}