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\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}
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In predicate logic there are:
\begin{itemize}
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\item variables $a,b,\ldots$ that represent \aemph{objects} (or \aemph{individuals}),
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\item \aemph{predicates} $P(x)$ or \aemph{relations} $R(x,y)$ on the objects \\
\end{itemize}
\end{goal}
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\begin{exampleblock}{}
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$1$-ary predicates like $P(\_)$ can express properties of objects:
\begin{itemize}
\item e.g. $P(x)$ can express that $x$ is green'
\end{itemize}
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$2$-ary predicates like $R(\_,\_)$ can express relations:
\begin{itemize}
\item e.g. $R(x,y)$ can express $x$ knows $y$'.
\end{itemize}
\end{exampleblock}
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\begin{goal}{}
Name natural examples of $3$-ary predicates?
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\begin{itemize}
\item $L(x,y,z)$ = $x,y,z$ are points on same line in the plane
\end{itemize}
\end{goal}
\end{frame}