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\documentclass[orivec]{llncs}

\usepackage[utf8]{inputenc}
\usepackage{url}
%\usepackage{tipa}
\usepackage{amsmath,amssymb,amstext}
\usepackage{graphicx,stmaryrd,mathabx,MnSymbol,tabularx,mathtools}
\usepackage[normalem]{ulem}
\usepackage{array}
\usepackage{mdframed}
\usepackage{wrapfig}
\usepackage{paralist}
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\usepackage{xspace}
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%\usepackage{appendix}

\usepackage[style=alphabetic,hyperref=auto,defernumbers=true,backend=bibtex,firstinits=true,maxbibnames=9,maxcitenames=3,isbn=false]{biblatex}
% \addbibresource{../../fr-macros/rabe.bib}
% \addbibresource{../../fr-macros/systems.bib}
% \addbibresource{../../fr-macros/pub_rabe.bib}
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\addbibresource{kwarcpubs.bib}
\addbibresource{extpubs.bib}
\addbibresource{kwarccrossrefs.bib}
\addbibresource{extcrossrefs.bib}
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\renewbibmacro*{event+venue+date}{}
\renewbibmacro*{doi+eprint+url}{%
  \iftoggle{bbx:doi}
    {\printfield{doi}\iffieldundef{doi}{}{\clearfield{url}}}
    {}%
  \newunit\newblock
  \iftoggle{bbx:eprint}
    {\usebibmacro{eprint}}
    {}%
  \newunit\newblock
  \iftoggle{bbx:url}
    {\usebibmacro{url+urldate}}
    {}}

\setlength{\hfuzz}{3pt} \hbadness=10001
\setcounter{tocdepth}{2} % for pdf bookmarks
\usepackage{xcolor}
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\usepackage{listings}
\lstset{columns=fullflexible,basicstyle=\sf}
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\usepackage[bookmarks,linkcolor=red,citecolor=blue,urlcolor=gray,colorlinks,breaklinks,bookmarksopen,bookmarksnumbered]{hyperref}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% local macros and configurations

% \usepackage{../../fr-macros/basics}
% \usepackage[llncs]{../../fr-macros/theorems}
% \input{macros}

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\def\cB{\mathcal{B}}
\def\cL{\mathcal{L}}
\def\defemph{\textbf}
\def\MMT{\textsf{MMT}\xspace}
\usepackage[show]{ed}
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\newif\ifshort\shorttrue

\pagestyle{plain} % remove for final version
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\author{Dennis Müller\inst{1} \and Florian Rabe\inst{1,2} \and Michael Kohlhase\inst{1}}
\institute{Computer Science, FAU Erlangen-N\"urnberg\and LRI, Universit\'e Paris Sud}

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\begin{document}

%\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\


\title{Alignment Finding}
\maketitle
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\begin{abstract}\ednote{tbw}
\end{abstract}

\setcounter{tocdepth}{2}\tableofcontents\newpage
\section{Introduction}\label{sec:intro}

\section{Applications}\label{sec:appl}

\subsection{Theory Classification}\label{sec:classifier}
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``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}
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\section{Conclusion}\label{sec:concl}
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\subsubsection*{Acknowledgements}
The authors gratefully acknowledge financial support from the OpenDreamKit Horizon 2020
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European Research Infrastructures project (\#676541) and the DFG-funded project OAF: An
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Open Archive for Formalizations (KO 2428/13-1).
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\renewcommand*{\bibfont}{\small}
\printbibliography

\end{document}

%%% Local Variables:
%%% mode: latex
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%  LocalWords:  inst maketitle formalization defs well-formedness textsf sec:impl impl
%  LocalWords:  sec:conc conc Universit printbibliography ednote Internalizing newpage
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%  LocalWords:  ifshort sec:relwork relwork renewcommand bibfont tbw setcounter tocdepth
%  LocalWords:  tableofcontents defemph compactenum emptyset newpart compactitem lstset
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%  LocalWords:  vdash baseset sec:concl subsubsection Formalizations