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

  \begin{exampleblock}{}
    \vspace{-1ex}
    \begin{talign}
      \myall{x}{\myex{y}{R(x,y)}}
    \end{talign}
    \pause
    This formula has a model; for example
    \begin{itemize}
      \item universe $\{1,2,3\}$ 
      \item $R(1,2)$, $R(2,3)$, $R(3,1)$ is true \; ($R(x,y)$ is false otherwise)
    \end{itemize}
    \medskip\pause
    
    We can draw this model as follows
    \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] (1) {1};
        \node [dot,below right of=1] (2) {2};
        \node [dot,above right of=2] (3) {3};
        \begin{scope}[->,thick]
        \draw (1) -- (2);
        \draw (2) -- (3);
        \draw (3) -- (1);
        \end{scope}
      \end{tikzpicture}
    \end{center}
    Here an \aemph{arrow} from $x$ to $y$ means $R(x,y)$.
    \medskip
  \end{exampleblock}
  \pause
  
  \begin{alertgoal}{}
    Is the following formula valid in this model?
    \begin{talign}
      \myex{y}{\myall{x}{R(x,y)}}
    \end{talign}
  \end{alertgoal}
\end{frame}