\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}