\begin{frame} \frametitle{Formulas and Logic Connectives} In predicate logic, the role of propositional variables is taken over by the \aemph{atomic formulas} with object/predicate-structure: \begin{goal}{} The \emph{atomic formulas} are predicates over objects: \begin{itemize} \item $P(x)$ \item $R(x,y)$ \end{itemize} \end{goal} \pause \begin{goal}{} Logic connectives $\;\neg,\; \vee,\; \wedge,\; \to\;$ keep their role. \end{goal} \pause \begin{block}{} We can build \emph{formulas} using propositional connectives, starting from the smallest building blocks of atomic formulas: \begin{itemize} \pause \item $P(x)$\quad\quad\pause\hint{($x$ is green)} \pause \item $P(x) \wedge R(x,y)$\quad\quad\pause\hint{($x$ is green and $x$ knows $y$)} \pause \item $R(x,y) \to \neg R(y,x)$\quad\quad\pause\hint{(if $x$ knows $y$ then $y$ does not know $x$)} \end{itemize} \end{block} \pause \begin{goal}{Predicate logic is more expressive} In propositional logic, we could only state $p$, $p \wedge q$, $p \to \neg q$. \end{goal} \end{frame}