\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}