\begin{frame}
  \frametitle{Examples: Semantics Intuitive}

  \begin{exampleblock}{}
    \vspace{-1ex}
    \begin{talign}
      \myex{x}{P(x)} \;\wedge\; \myall{x}{\big(P(x) \to \myex{y}{(Q(y) \wedge R(x,y))}\big)}
    \end{talign}
    \pause
    Assume the following meaning of the predicates:
    \begin{itemize}
      \item $P(x)$ = `$x$ is green', 
      \item $Q(x)$ = `$x$ is red', and
      \item $R(x,y)$ = `$x$ knows $y$'.
    \end{itemize}
    \pause\medskip
    What does the formula mean?
    \pause
    \begin{itemize}
      \item there exists a green element, and
      \item every green element knows a red element.
    \end{itemize}
    \pause\medskip
    Find a model for this formula!
    \pause
    \begin{center}
      \begin{tikzpicture}[node distance=15mm,
        dot/.style={minimum size=4mm, circle, draw=none, fill=black, inner sep=0, outer sep=1mm, text=white}]
        \node [dot,fill=mgreen] (1) {1};
        \node [dot,below right of=1,fill=mred] (2) {2};
        \node [dot,above right of=2] (3) {3};
        \begin{scope}[->,thick]
        \draw (1) -- (2);
        \end{scope}
      \end{tikzpicture}
    \end{center}
  \end{exampleblock}
\end{frame}