\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}