\begin{frame} \frametitle{Introduction} \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] {}; \node [lo=3] {$w_3$}; \node (2) [point, below right of=3] {\alt<-2>{$\lab{q}$}{}}; \node [aro=2] {$w_2$}; \node (1) [point, below left of=3] {$\lab{q}$}; \node [alo=1] {$w_1$}; \begin{scope}[shorten <= 1mm, shorten >= 1mm, very thick,>=stealth] \draw [->] (1) to (3); \draw [->] (3) to (2); \draw [->] (3) to[out=45,in=45+90,looseness=4] (3); \end{scope} \draw [rounded corners=2mm, dashed] (-25mm,-20mm) rectangle (25mm,11mm); \node at (-25mm,8mm) [anchor=north east,inner sep=2mm] {$\mathcal{M}_{\alt<-2>{1}{2}}$}; \end{tikzpicture} \end{center} \end{minipage} \begin{minipage}{0.49\textwidth} \begin{talign} \onslide<-2>{ w_2 &\fc \all\some q \\ w_3 &\fc q \to \all\some q \\ w_2 &\fc q \\ w_3 &\fc \some q \\ w_1 &\fc \all\some q \\[1ex] } \M_1 & \models q \to \all\some q \\ \mpause[2]{ \M_2 & \not\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Can you change the labelling such that such that \begin{talign} \M \models q \to \all\some q \end{talign} is no longer valid?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 Yes, for example, by setting $\lab{L}(w_2) = \{\; \}$\;. \end{frame}