\begin{frame}[t]
  \frametitle{How to interpret formulas in predicate logic?}
  
  Simple formulas in predicate logic:  
  \begin{itemize}
    \item $\formula{\binpred{R}{\const{a}}{\const{b}}}$
    \item $\formula{\forallst{x}{(\logor{\unpred{P}{x}}{\unpred{Q}{x}})}}$
    \item $\formula{\forallst{x}{\, (x \mathrel{\sbinpred{\le}} {x \mathrel{\sfunc{\boldsymbol{\cdot}}} \const{e}}) }}$ 
  \end{itemize}
      
  What can we say about their \emph{meaning} and \emph{truth values}?\pause{}
  \medskip
  
  \begin{goal}{}
    These depend on:
    \begin{itemize}
      \item
        the domain of quantification
      \pause
      \item  
        the interpretation of the predicate symbols $\sbinpred{R},\, \sunpred{P},\, \sunpred{Q},\, \sbinpred{\le}$
      \pause
      \item
        the interpretation of the constants $\const{a},\,\const{b},\,\const{e}$
      \pause
      \item
        the interpretation of the function symbol $\,\sfunc{\boldsymbol{\cdot}}\,$
    \end{itemize}
  \end{goal}
  \pause\medskip
  
  Different interpretations can make these formulas true or false.
  \pause\medskip
  
  We need a concept of \emph{model} for the interpretation of formulas. 
\end{frame}