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\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}