structuring

tex/intro.tex

+``Semantic Search'' -- a very suggestive term, which is alas seriously under-defined --
+has often been touted as the ``killer application'' of semantic technologies. With a view
+finder, we can add another possible interpretation: searching mathematical ontologies
+(here modular theorem prover libraries) at the level of theories -- we call this \defemph{theory
+classification}.
+
+The basic use case is the following: Jane, a mathematician, becomes interested in a class
+of mathematical objects, say -- as a didactic example -- something she initially calls
+``beautiful subsets'' of a base set $\cB$ (or just ``beautiful over $\cB$''). These have
+the following properties:
+\begin{compactenum}
+\item the empty set is beautiful over $\cB$
+\item every subset of a beautiful set is beautiful over $\cB$
+\item If $A$ and $B$ are beautiful over $\cB$and $A$ has more elements than $B$, then
+  there is an $x\in A\backslash B$, such that $B\cup\{x\}$ is beautiful over $\cB$.
+\end{compactenum}
+To see what is known about beautiful sets, she types these three conditions into a theory
+classifier, which interprets them as a \MMT theory $Q$, computes all (total) views from
+$Q$ into a library $\cL$, and returns presentations of target theories and the assignments
+made by the views. In our example we have the situation in
+Figure~\ref{fig:theory-classification-ex}\ednote{MK: Maybe better do this in jEdit and use
+  screenshots} \ednote{Interesting: the $\emptyset$ clause could also be ``$\exists S$
+  beautiful'', which is equivalent via the subset clause, maybe use that in the example:
+  define Matroid with that and have a theorem that says that $\emptyset$ is beautiful. Just
+  see what the viewfinder catches.}  In the base use case, Jane learns that her
+``beautiful sets'' correspond to the well-known structure of
+matroids~\cite{wikipedia:matroid}, so she can directly apply matroid theory to her
+problems.
+
+\begin{newpart}{MK: this could/should be extended}
+  In extended use cases, we could
+\begin{compactitem}
+\item use partial views to find theories that share significant structure with $Q$, so
+  that we can formalize $Q$ with modularly with minimal effort. Say Jane was interested in
+  ``dazzling subsets'', i.e. beautiful subsets that obey a fourth condition, then she
+  could just contribute a theory that extends \textsf{matroid} by a formalization of the
+  fourth condition -- and maybe rethink the name.
+\item use existing views in $\cL$ (compositions of views are vivews) to give Jane more
+  information about her beautiful subsets, e.g. that matroids (and thus beautiful sets)
+  form a generalization of the notion of linear independence from linear algebra.
+\end{compactitem}
+\end{newpart}
+
+\begin{figure}[ht]\centering\lstset{aboveskip=0pt,belowskip=0pt}
+\begin{tabular}{|p{5cm}|p{5cm}|}\hline
+  $Q$ & Result \\\hline
+\begin{lstlisting}[mathescape]
+theory query :  F?MitM
+   include ?set
+   Base : {A} set A
+   beautiful {A} set A $\rightarrow$ prop
+   empty : $\vdash$ beautiful $\emptyset$ 
+   subset-closed: $\vdash$ {}
+\end{lstlisting}
+& 
+\begin{lstlisting}[mathescape]
+theory matroid :  F?MitM
+   include ?baseset
+   independent {A} set A $\rightarrow$ 
+   empty: $\vdash$
+   hereditary : $\vdash$
+   augmentation: $\vdash$
+\end{lstlisting}
+\\\hline
+\end{tabular}
+\caption{Theory Classification for beautiful sets}\label{fig:theory-classification-ex}
+\end{figure}

tex/paper.tex

@@ -72,78 +72,14 @@
 \end{abstract}
 
 \setcounter{tocdepth}{2}\tableofcontents\newpage
-\section{Introduction}\label{sec:intro}
-
-\section{Applications}\label{sec:appl}
-
-\subsection{Theory Classification}\label{sec:classifier}
-``Semantic Search'' -- a very suggestive term, which is alas seriously under-defined --
-has often been touted as the ``killer application'' of semantic technologies. With a view
-finder, we can add another possible interpretation: searching mathematical ontologies
-(here modular theorem prover libraries) at the level of theories -- we call this \defemph{theory
-classification}.
-
-The basic use case is the following: Jane, a mathematician, becomes interested in a class
-of mathematical objects, say -- as a didactic example -- something she initially calls
-``beautiful subsets'' of a base set $\cB$ (or just ``beautiful over $\cB$''). These have
-the following properties:
-\begin{compactenum}
-\item the empty set is beautiful over $\cB$
-\item every subset of a beautiful set is beautiful over $\cB$
-\item If $A$ and $B$ are beautiful over $\cB$and $A$ has more elements than $B$, then
-  there is an $x\in A\backslash B$, such that $B\cup\{x\}$ is beautiful over $\cB$.
-\end{compactenum}
-To see what is known about beautiful sets, she types these three conditions into a theory
-classifier, which interprets them as a \MMT theory $Q$, computes all (total) views from
-$Q$ into a library $\cL$, and returns presentations of target theories and the assignments
-made by the views. In our example we have the situation in
-Figure~\ref{fig:theory-classification-ex}\ednote{MK: Maybe better do this in jEdit and use
-  screenshots} \ednote{Interesting: the $\emptyset$ clause could also be ``$\exists S$
-  beautiful'', which is equivalent via the subset clause, maybe use that in the example:
-  define Matroid with that and have a theorem that says that $\emptyset$ is beautiful. Just
-  see what the viewfinder catches.}  In the base use case, Jane learns that her
-``beautiful sets'' correspond to the well-known structure of
-matroids~\cite{wikipedia:matroid}, so she can directly apply matroid theory to her
-problems.
-
-\begin{newpart}{MK: this could/should be extended}
-  In extended use cases, we could
-\begin{compactitem}
-\item use partial views to find theories that share significant structure with $Q$, so
-  that we can formalize $Q$ with modularly with minimal effort. Say Jane was interested in
-  ``dazzling subsets'', i.e. beautiful subsets that obey a fourth condition, then she
-  could just contribute a theory that extends \textsf{matroid} by a formalization of the
-  fourth condition -- and maybe rethink the name.
-\item use existing views in $\cL$ (compositions of views are vivews) to give Jane more
-  information about her beautiful subsets, e.g. that matroids (and thus beautiful sets)
-  form a generalization of the notion of linear independence from linear algebra.
-\end{compactitem}
-\end{newpart}
-
-\begin{figure}[ht]\centering\lstset{aboveskip=0pt,belowskip=0pt}
-\begin{tabular}{|p{5cm}|p{5cm}|}\hline
-  $Q$ & Result \\\hline
-\begin{lstlisting}[mathescape]
-theory query :  F?MitM
-   include ?set
-   Base : {A} set A
-   beautiful {A} set A $\rightarrow$ prop
-   empty : $\vdash$ beautiful $\emptyset$ 
-   subset-closed: $\vdash$ {}
-\end{lstlisting}
-& 
-\begin{lstlisting}[mathescape]
-theory matroid :  F?MitM
-   include ?baseset
-   independent {A} set A $\rightarrow$ 
-   empty: $\vdash$
-   hereditary : $\vdash$
-   augmentation: $\vdash$
-\end{lstlisting}
-\\\hline
-\end{tabular}
-\caption{Theory Classification for beautiful sets}\label{fig:theory-classification-ex}
-\end{figure}
+
+\section{Introduction}\label{sec:intro}\input{intro}
+
+\section{Preliminaries}\label{sec:prelim}\input{prelim}
+
+\section{Viewfinder}\label{sec:viewfinder}\input{viewfinder}
+
+\section{Extended Use Case}\label{sec:usecase}\input{usecase}
 
 \section{Conclusion}\label{sec:concl}
 

tex/prelim.tex

+MMT theories, flat, bla
\ No newline at end of file