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\begin{frame}
\frametitle{Semantic Implication}

\begin{goal}{Semantic Implication / Consequence}
\vspace{-1ex}
\begin{talign}
\end{talign}
means
\begin{center}
Whenever $\phi_1,\ldots,\phi_n$ are all true, $\psi$ is also true.
\end{center}
\end{goal}
\bigskip
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\begin{exampleblock}{}
Do we have \quad $q \;\models\; p \to q$ \quad ?
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\begin{center}
\begin{tabular}{|c|c|c|}
\hline
\thd $p$ & \thd $q$ & \thd $p \to q$ \\
\hline
$\F$ & $\F$ & $\T$\\
\hline
$\F$ & \malert{1}{4}{$\T$} & \malert{2}{3}{$\T$}\\
\hline
$\T$ & $\F$ & $\F$\\
\hline
$\T$ & \malert{1}{4}{$\T$} & \malert{2}{3}{$\T$}\\
\hline
\end{tabular}
\end{center}
\pause\pause\pause
Whenever $q$ is $\T$ also $p \to q$ is $\T$.
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Hence: $q \;\models\; p \to q$\;.
\end{exampleblock}
\end{frame}