\frametitle{Examples: Semantics Intuitive}

  \begin{goal}{Semantics Intuitive}
    The semantics of a predicate logic formula are \emph{models}.
    A \emph{model} for a formula consists of
      \item a \emph{universe} of objects/individuals
      \item \emph{predicates} / \emph{relations} over the universe
    such that the formula holds in this model.
    This formula has a \emph{model}; for example
      \item universe $\{1,2,3\}$ 
      \item $P(1)$,\; $\neg P(2)$,\; $\neg P(3)$
    In a picture, this looks as follows:
      \item a \aemph{green dot} indicates that $P$ is $\T$ 
      \begin{tikzpicture}[dot/.style={minimum size=4mm, circle, draw=none, fill=black, inner sep=0, outer sep=1mm, text=white}]
        \node [dot,fill=mgreen] (1) {1};
        \node [dot,below right of=1] (2) {2};
        \node [dot,above right of=2] (3) {3};