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

\begin{exampleblock}{}
\vspace{-1ex}
\begin{talign}
\myall{x}{\myall{y}{(R(x,y) \vee R(y,x))}}
\end{talign}
\pause
Find a model for this formula!
\pause
\begin{tcenter}
\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 (1) -- (3);
\draw (2) to[out=-45,in=-45-90,looseness=5] (2);
\draw (1) to[out=45+90,in=45+180,looseness=5] (1);
\draw (3) to[out=45,in=45-90,looseness=5] (3);
\end{scope}
\end{tikzpicture}
\end{tcenter}
\pause

Other examples of models for this formula:\vspace{-1ex}
\begin{tcenter}
\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,right of=1] (2) {2};
\begin{scope}[->,thick]
\draw (1) -- (2);
\draw (1) to[out=45+90,in=45+180,looseness=5] (1);
\draw (2) to[out=45,in=45-90,looseness=5] (2);
\end{scope}
\end{tikzpicture}
\end{tcenter}
\pause
or a model with one element (universe is always non-empty):\vspace{-1ex}
\begin{tcenter}
\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};
\begin{scope}[->,thick]
\draw (1) to[out=45+90,in=45+180,looseness=5] (1);
\end{scope}
\end{tikzpicture}\vspace{-2ex}
\end{tcenter}
\end{exampleblock}
\end{frame}