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\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 black 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}