\begin{frame} \frametitle{Parse Trees} \begin{exampleblock}{ We make a parse tree from the formula $$\myex{y}{ \myall{z}{ (\myex{x}{R(x,z)} \to (R(x,z) \wedge R(y,z))) }}$$ } \pause \begin{center} \tikz[level distance=9mm, level 1/.style={sibling distance=20mm}, level 2/.style={sibling distance=35mm}, level 3/.style={sibling distance=30mm}, level 4/.style={sibling distance=17mm}, level 5/.style={sibling distance=8mm}, ] \node {$\exists y$} child {node {$\forall z$} child {node {$\to$} child {node {$\exists x$} child {node {$R$} child {node {$x$} } child {node {$z$} } } } child {node {$\wedge$} child {node {$R$} child {node {$x$} } child {node {$z$} } } child {node {$R$} child {node {$y$} } child {node {$z$} } } } } }; \end{center} \end{exampleblock} \pause \begin{alertblock}{} The $x$ on the left is in the scope of $\exists x$; the $x$ in the middle not. \end{alertblock} \end{frame}