\begin{frame} \frametitle{Predicate Logic} \begin{goal}{} In propositional logic there are: \begin{itemize} \item propositional variables $p,q,r,\ldots$ that can be $\T$ or $\F$ \end{itemize} \medskip \pause In predicate logic there are: \begin{itemize} \pause \item variables $a,b,\ldots$ that represent \aemph{objects} (or \aemph{individuals}), \pause \item \aemph{predicates} $P(x)$ or \aemph{relations} $R(x,y)$ on the objects \\ \end{itemize} \end{goal} \pause \smallskip \begin{exampleblock}{} \pause $1$-ary predicates like $P(\_)$ can express properties of objects: \begin{itemize} \item e.g. $P(x)$ can express that `$x$ is green' \end{itemize} \pause $2$-ary predicates like $R(\_,\_)$ can express relations: \begin{itemize} \item e.g. $R(x,y)$ can express `$x$ knows $y$'. \end{itemize} \end{exampleblock} \pause \smallskip \begin{goal}{} Name natural examples of $3$-ary predicates? \pause \begin{itemize} \item $L(x,y,z)$ = $x,y,z$ are points on same line in the plane \end{itemize} \end{goal} \end{frame}