\begin{frame} \frametitle{Examples: Semantics Intuitive} \begin{alertgoal}{} This is a typical exam task! \end{alertgoal} \begin{exampleblock}{} \vspace{-1ex} \begin{talign} & \myall{x}{\myall{y}{\big(R(x,y) \vee R(y,x)\big)}} \\ & \wedge \myall{x}{\myall{y}{\myall{z}{\big(R(x,y) \wedge R(y,z) \to R(x,z)\big)}}} \\ & \wedge \myall{x}{\myex{y}{\neg R(x,y)}} \end{talign} \pause Find a model for this formula, or explain why there is none. \medskip \pause This formula has a model: \begin{itemize} \item universe $\nat = \{0,1,2,3,4,5\ldots\}$ \item $R(x,y)$ if $x \ge y$ \end{itemize} \pause We check that the formula holds in the model: \begin{itemize} \pause \item for all $x,y \in \nat$, we have $x \ge y \vee y \ge x$ \pause \item for all $x,y,z \in \nat$, we have $x \ge y \wedge y \ge z \to x \ge z$ \pause \item for every $x\in\nat$ there is $y\in\nat$ such that $x \not\ge y$ \end{itemize} \end{exampleblock} \end{frame}