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@@ -44,4 +44,71 @@ and how would need to proceed if one would like to extend it to large datasets o
 real-time operation.
 
 
-\fi
\ No newline at end of file
+\fi
+\section{Domain representation}
+Translating the domain specification to AILog results in the following AILog
+code:
+\inputminted[linenos,fontsize=\footnotesize]{prolog}{./src/pizza.ail}
+
+\section{Queries}
+\subsection{Initial probabilities}
+Chances for shapes to be present are visible in Table~\ref{chances} and from
+that we can calculate all the initial probabilites for all the shapes for
+example with the following queries:
+\begin{minted}[fontsize=\footnotesize]{prolog}
+ailog: predict circle.
+Answer: P(circle|Obs)=0.01.
+       [ok,more,explanations,worlds,help]: ok.
+ailog: observe circle.
+Answer: P(circle|Obs)=0.01.
+       [ok,more,explanations,worlds,help]: ok.
+ailog: predict circlePresent.
+Answer: P(circlePresent|Obs)=0.95.
+       [ok,more,explanations,worlds,help]: ok.
+\end{minted}
+\begin{table}
+       \label{chances}
+       \begin{tabular}{|l|ll|}
+               \hline
+               & Observed\\
+               Present & T & F\\
+               \hline
+               T & $0.95$ & $0.01$\\
+               F & $0.05$ & $0.99$\\
+               \hline
+       \end{tabular}
+\end{table}
+
+\subsection{Querying probabilites for pizzas}
+Since the chance of a false positive on a shape is so low the initial
+probabilities for pizza types are very low. When certain shapes that belong to
+a certain type of pizza occur the probability improves a lot. We can show this
+by showing the probabilites of a pepperoni pizza before, during and after
+observing the ingredients with the following queries:
+\begin{minted}[fontsize=\footnotesize]{prolog}
+ailog: predict p_pepperoni.
+Answer: P(p_pepperoni|Obs)=0.0019.
+       [ok,more,explanations,worlds,help]: ok.
+ailog: observe circle.
+Answer: P(circle|Obs)=1.0.
+       [ok,more,explanations,worlds,help]: ok.
+ailog: predict p_pepperoni.
+Answer: P(p_pepperoni|Obs)=0.0019.
+       [ok,more,explanations,worlds,help]: ok.
+ailog: observe doublecircle.
+Answer: P(doublecircle|Obs)=0.01.
+       [ok,more,explanations,worlds,help]: ok.
+ailog: predict p_pepperoni.
+Answer: P(p_pepperoni|Obs)=0.19.
+       [ok,more,explanations,worlds,help]: ok.
+\end{minted}
+
+\subsection{Finding out which pizza is the most likely to be present on the
+image}
+We do not only want to know what the probability for a specific pizza is but
+also the most likely pizza so that we can give an educated guess about the
+pizza type present on the image processed. This can be done with the following
+queries:
+
+
+\section{Reflections}