\begin{frame} \frametitle{Truth of Diamonds: $\some \phi$} \begin{goal}{$w \fc \some \phi$} The formula \;\;$\some \phi$ is true in world $w$\;\; if there exists a world $w'$\;\; such that \;\;$R(w,w')$ \;\;and\;\; $\phi$ is true in $w'$. \end{goal} \pause \begin{block}{} As a formula:\quad $w \fc \some \phi \quad\DARKRED{\iff}\quad \myex{w'}{\big( R(w,w') \;\wedge\; w' \fc \phi \big)}$ \end{block} \pause \begin{exampleblock}{} \exampleA For example, \begin{talign} \mpause[1]{ w_1 &\mpause{\fc} \some\lab{p} } & \mpause{ w_3 &\mpause{\notfc} \some\lab{p} } & \mpause{ w_1 &\mpause{\fc} \some\lab{q} } & \mpause{ w_3 &\mpause{\fc} \some\lab{q} } \end{talign} \end{exampleblock} \end{frame}