\begin{frame}{Example (2)} \begin{exampleblock} {\black{$\asetfuncs = \emptyset$, $\,\asetpreds = \setexp{ \sbinpred{R}{\alt<1-4>{{\scriptstyle /2}}{\alert{\scriptstyle /2}}}}$}} \pause{} \vspace*{1ex} Illustration of a model: \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 (3) -- (2); \draw (2) to[out=-45,in=-45-90,looseness=5] (2); \end{scope} \draw [rounded corners=5mm,thick,dashed] ($(1) + (-6mm,5mm)$) rectangle ($(3) + (6mm,-20mm)$); \uncover<3->{\node [right of=3,node distance=10mm,yshift=6.5mm] {{$\model{\amodel}$}};} \uncover<4->{\node [right of=2,node distance=8.5mm,yshift=-2mm] {$\model{\adomain}$};} \end{tikzpicture} \end{center} \pause{} Formal definition of $\model{\amodel}$: \pause{} \begin{itemize} \item domain $\model{\adomain} = \setexp{1,2,3}$ \pause{} \item interpretation operation $(\cdot)^{\model{\amodel}}$ on $\pair{\asetfuncs}{\asetpreds}$: \begin{itemize} \item $\sbinpred{R}$ is \alert{binary predicate}: \\[.5ex] $\intin{\sunpred{R}}{\model{\amodel}} \uncover<5->{= \setexp{ \pair{1}{2},\, \pair{2}{2},\, \pair{3}{2} }} \alert{\subseteq \adomain \times \adomain}$. \end{itemize} \end{itemize} \end{exampleblock} \end{frame}