\begin{frame} \frametitle{Examples: Semantics Intuitive} \begin{exampleblock}{} \vspace{-1ex} \begin{talign} \myall{x}{\myex{y}{R(x,y)}} \end{talign} \pause This formula has a model; for example \begin{itemize} \item universe $\{1,2,3\}$ \item $R(1,2)$, $R(2,3)$, $R(3,1)$ is true \; ($R(x,y)$ is false otherwise) \end{itemize} \medskip\pause We can draw this model as follows \begin{center} \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 (3) -- (1); \end{scope} \end{tikzpicture} \end{center} Here an \aemph{arrow} from $x$ to $y$ means $R(x,y)$. \medskip \end{exampleblock} \pause \begin{alertgoal}{} Is the following formula valid in this model? \begin{talign} \myex{y}{\myall{x}{R(x,y)}} \end{talign} \end{alertgoal} \end{frame}