\begin{frame}{Reachability via $\sbinpred{R}$}
  \begin{goal}{}
    For a binary predicate symbol $\sbinpred{R}$ we want to express:
    \begin{center}
      \sentence{$v$ is reachable via $\sbinpred{R}$ from $u$}
      \smallskip
    \end{center}
  \end{goal}
  \pause
  Thinking of $\sbinpred{R}$ as arrows, this means:
  there is a path from $v$ to $u$.\\
  \pause\bigskip
    
  \begin{exampleblock}{Example}  
    If we consider the relation $\sbinpred{R}\,$:  
    \begin{center}
      $\binpred{R}{\freevar{x}}{\freevar{y}}\;$: $\;\;$
      $\freevar{x}$ is child of $\freevar{y}$
    \end{center}\pause{}
    Then reachability via $\sbinpred{R}$ is the relation:
    \begin{center}
      `$x$ is descendant of, or is the same person as $y$'
    \end{center}
  \end{exampleblock}
\end{frame}