\begin{frame}
  \frametitle{Non-Monotonic Behaviour}
  
  In natural language, queries that contain formulations like 
  \begin{align*}
    &  
    \begin{aligned}
      & \text{``\emph{there is no}''} \\
      & \text{``\emph{does not exists}''}    
    \end{aligned} 
    && \Bigg\} && 
    \begin{aligned}
      & \text{\emph{negated existential}} \\[-.7ex]
      & \text{\emph{quantification}}
    \end{aligned}
    \\[1ex]
    & 
    \begin{aligned}
      & \text{``\emph{for all}''} \\
      & \text{``\emph{the minimum/maximum}''}
    \end{aligned}
    && \Bigg\} && \emph{universally quantification}
  \end{align*}
  indicate non-monotonic behaviour.
  \pause\bigskip

  \begin{goal}{}
    In an equivalent SQL formulation of such queries, this
    boils down to a \emph{test whether a query yields a (non-)empty result.}
  \end{goal}
\end{frame}

\theme{Not In}