\begin{frame} \frametitle{Predicate Logic: Syntax} \begin{goal}{} The \aemph{atomic formulas} such as $P(a)$, $R(a,b)$,\ldots,$P(x)$,$R(x,y)$ are the building blocks of formulas: \begin{itemize} \item here $P$, $R$, \ldots are the \aemph{predicate symbols}, \item $a,b,c,\ldots$ are \aemph{constants}, \item $x,y,z,\ldots$ are \aemph{variables}. \end{itemize} \end{goal} \pause\smallskip \begin{goal}{} Complex formulas can be build from: \begin{itemize} \pause \item atomic formulas, \pause \item connectives $\;\neg,\; \vee,\; \wedge,\; \to\;$ to connect fomulas \begin{talign} \neg \phi && \phi \vee \psi && \phi \wedge \psi && \phi \to \psi \end{talign}\vspace{-2ex} \pause \item quantifiers $\forall x$, $\forall y$, \ldots and $\exists x$, $\exists y$, \ldots \begin{talign} \myall{x}{\phi} && \myex{x}{\phi} \end{talign} \end{itemize} \end{goal} \end{frame}