\begin{frame} \frametitle{Semantic Implication / Entailment} \begin{goal}{We define \;\;$ \phi_1, \ldots, \phi_n \; \models \; \psi $\;\; as} In \aemph{every world} $w$ in \aemph{every Kripke model} $\mathcal{M}$ where \begin{center} $\mathcal{M},w \models \phi_1$ and $\ldots$ and $\mathcal{M},w \models \phi_n$ \end{center} it holds also \begin{talign} \mathcal{M},w \models \psi \end{talign} \end{goal} \smallskip \pause \begin{exampleblock}{} \begin{malign} \mpause[1]{\all p \;\mpause{&\not\models}\; \some p } \\ \mpause{\all p,\; \some q \;\mpause{&\models}\; \some p } \\ \mpause{\all\some p \;\mpause{&\not\models}\; \some\all p } \\ \mpause{\some\all p \;\mpause{&\not\models}\; \all\some p } \\ \mpause{\all (p \to q),\; \some p \;\mpause{&\models}\; \some q } \end{malign} \end{exampleblock} \end{frame}