\begin{frame} \frametitle{Another Example} \begin{minipage}{0.5\textwidth} \begin{center} \begin{tikzpicture}[ default, point/.style={circle, draw=blue, thick, inner sep=3pt, minimum size=9mm}, node distance=20mm] \node (3) [point] {$\lab{p,r}$}; \node [ao=3] {$w_3$}; \node (2) [point, below right of=3,yshift=-5mm] {$\lab{q}$}; \node [aro=2] {$w_2$}; \node (1) [point, below left of=3,yshift=-5mm] {$\lab{p}$}; \node [alo=1] {$w_1$}; \begin{scope}[shorten <= 1mm, shorten >= 1mm, very thick,>=stealth] \draw [->] (1) to[bend left=15] (2); \draw [->] (2) to[bend left=15] (1); \draw [->] (2) to[bend left=15] (3); \draw [->] (3) to[bend left=15] (2); \draw [->] (3) to[bend left=15] (1); \draw [->] (1) to[bend left=15] (3); \end{scope} \draw [rounded corners=2mm, dashed] (-25mm,-25mm) rectangle (25mm,10mm); \node at (-25mm,8mm) [anchor=north east,inner sep=2mm] {$\mathcal{M}_3$}; \end{tikzpicture} \end{center} \end{minipage} \begin{minipage}{0.49\textwidth} \begin{talign} w_1 &\fc \some q \\ w_3 &\fc \some q \\ w_2 &\fc \all\some q \\[1ex] \M_3 & \models q \to \all\some q \end{talign} \end{minipage} \smallskip\pause \begin{alertblock}{Question} Can you change the labelling such that such that \begin{talign} \M \models q \to \all\some q \end{talign} is no longer valid? \end{alertblock} \pause\smallskip Answer: \aemph{No}, that is not possible. \end{frame}