\begin{frame} \frametitle{A \emph{Frame} is a Kripke Model without Labelling} \begin{goal}{} A \emph{frame} $\mathcal{F} = (\BLUE{W},R)$ consists of \begin{itemize} \item $\BLUE{W}$, the worlds \item $R$, the accessibility relation \end{itemize} \end{goal} \begin{exampleblock}{} \begin{center} \begin{tikzpicture}[ default, point/.style={circle, draw=blue, thick, inner sep=3pt, minimum size=7mm}, node distance=17mm] \node (3) [point] {}; \node [ao=3] {$w_3$}; \node (2) [point, below right of=3,yshift=-5mm] {}; \node [aro=2] {$w_2$}; \node (1) [point, below left of=3,yshift=-5mm] {}; \node [alo=1] {$w_1$}; \begin{scope}[shorten <= 1mm, shorten >= 1mm, very thick,>=stealth] \draw [->] (1) to (2); \draw [->] (1) to (3); \draw [->] (3) to (2); \end{scope} \draw [rounded corners=2mm, dashed] (-25mm,-23mm) rectangle (25mm,10mm); \node at (-25mm,8mm) [anchor=north east,inner sep=2mm] {$\mathcal{F}$}; \end{tikzpicture} \end{center} \vspace{-2ex} \begin{itemize} \item $\BLUE{W}= \{\; w_1,\; w_2,\; w_3 \; \}$ \item $R = \{ \;\pair{w_1}{w_2},\; \pair{w_1}{w_3},\; \pair{w_3}{w_2}\; \}$ \end{itemize} \end{exampleblock} \pause \begin{goal}{} A Kripke model $\M$ is a frame $\F = (W,R)$ plus a labelling $L$. \end{goal} \end{frame}