\begin{frame}{A Simple Model}

  \begin{exampleblock}{\black{$\asetfuncs = \setexp{ \const{c}{\scriptstyle /0} }$,
                              $\asetpreds = \setexp{ \sunpred{P}{\scriptstyle /1}, \, \sbinpred{R}{\scriptstyle /2} }$}}
    \pause{}                          
    
    \hspace*{-1ex}
    \begin{minipage}{0.59\textwidth}
      
    \scalebox{.8}{  
    \begin{tikzpicture}[point/.style={circle,fill=black!60!white,draw=none,inner sep=2pt,minimum size=4mm},
       node distance=26mm]
      \node (1) [point] {};
      \alt<1-2>{
      \node (3) [point,fill,%green!50!black, 
                       below right of =1] {};}{
      \node (3) [point,fill=forestgreen,%green!50!black, 
                       below right of =1] {};}
      \node (2) [point, above right of=3] {};
      % \node at ($(1)!.5!(2) + (0mm,-20mm)$) {A};
      \node at (1) [xshift=-6mm] {$a_1$};
      \node at (2) [xshift=6mm] {$a_2$};
      \node at (3) [xshift=5mm] {$a_3$};
   
      \uncover<5->{    
      \begin{scope}[shorten <= 2mm, shorten >= 2mm, very thick, >=stealth]
      \draw [->] (3) to[out=-140,in=-40,looseness=10] (3);
      \draw [->] (1) to (2);
       \draw [->] (1) to (3);
       \draw [->] (3) to (2);
      \end{scope}}
      
      \uncover<4->{
      \begin{scope}[circ/.style={circle,draw=mediumblue,very thick,inner sep=0,minimum size=6mm}]
        \node at (1) [circ] {};
        \node at (2) [circ] {};    
      \end{scope}}
      \node [left of=1,node distance=17mm,yshift=8mm] {\Large $\model{\amodel}$};
      \draw [rounded corners=5mm,thick,dashed] 
                 ($(1) + (-12mm,10mm)$) rectangle ($(2) + (12mm,-32mm)$);
    \end{tikzpicture}
    }
    \end{minipage}
    \hspace*{-2ex}
    \begin{minipage}{0.43\textwidth}
    %   
    \begin{itemize}    
      \item<3-> 
        $\intin{\const{c}}{\model{\amodel}}$: $\,$ \textcolor{forestgreen}{green} point
      \item<4->  
        $\intin{\sunpred{P}}{\model{\amodel}}$: $\,$ \textcolor{mediumblue}{blue} circles
      \item<5->   
        $\intin{\sbinpred{R}}{\model{\amodel}}$: $\,$ arrows
    \end{itemize}  
    \end{minipage}
   
    \bigskip 
  
    \uncover<5->{is a model $\model{\amodel}$ with:}
    \begin{itemize}  
      \item<6->  
        domain $\model{\adomain} = \{a_1,a_2,a_3\}$
      \item<7->  
        $\intin{\const{c}}{\model{\amodel}} = a_3$
      \item<8->  
        $\intin{\sunpred{P}}{\model{\amodel}} = \{a_1,a_2\}$
      \item<9->  
        $\intin{\sbinpred{R}}{\model{\amodel}} = \bigl\{\langle a_1,a_2\rangle ,\langle a_1,a_3\rangle ,
          \langle a_3,a_2\rangle ,\langle a_3,a_3\rangle \bigr\}$
    \end{itemize} 
  
  \end{exampleblock}   
  
\end{frame}

\theme{Interpretation \\[1ex]
  {\large of formulas \alert{without} quantifiers and free variables}}