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OAF
alignmentfinder
Commits
6b983337
Commit
6b983337
authored
Apr 04, 2018
by
Michael Kohlhase
Browse files
use case
parent
495890c3
Changes
1
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tex/paper.tex
View file @
6b983337
...
...
@@ 10,13 +10,17 @@
\usepackage
{
mdframed
}
\usepackage
{
wrapfig
}
\usepackage
{
paralist
}
\usepackage
{
xspace
}
%\usepackage{appendix}
\usepackage
[style=alphabetic,hyperref=auto,defernumbers=true,backend=bibtex,firstinits=true,maxbibnames=9,maxcitenames=3,isbn=false]
{
biblatex
}
% \addbibresource{../../frmacros/rabe.bib}
% \addbibresource{../../frmacros/systems.bib}
% \addbibresource{../../frmacros/pub_rabe.bib}
% \addbibresource{../../kwarc.bib}
\addbibresource
{
kwarcpubs.bib
}
\addbibresource
{
extpubs.bib
}
\addbibresource
{
kwarccrossrefs.bib
}
\addbibresource
{
extcrossrefs.bib
}
\renewbibmacro*
{
event+venue+date
}{}
\renewbibmacro*
{
doi+eprint+url
}{
%
\iftoggle
{
bbx:doi
}
...
...
@@ 34,7 +38,8 @@
\setlength
{
\hfuzz
}{
3pt
}
\hbadness
=10001
\setcounter
{
tocdepth
}{
2
}
% for pdf bookmarks
\usepackage
{
xcolor
}
\usepackage
{
listings
}
\lstset
{
columns=fullflexible,basicstyle=
\sf
}
\usepackage
[bookmarks,linkcolor=red,citecolor=blue,urlcolor=gray,colorlinks,breaklinks,bookmarksopen,bookmarksnumbered]
{
hyperref
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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@@ 44,7 +49,11 @@
% \usepackage[llncs]{../../frmacros/theorems}
% \input{macros}
\usepackage
[hide]
{
ed
}
\def\cB
{
\mathcal
{
B
}}
\def\cL
{
\mathcal
{
L
}}
\def\defemph
{
\textbf
}
\def\MMT
{
\textsf
{
MMT
}
\xspace
}
\usepackage
[show]
{
ed
}
\newif\ifshort\shorttrue
\pagestyle
{
plain
}
% remove for final version
...
...
@@ 68,12 +77,79 @@
\section
{
Applications
}
\label
{
sec:appl
}
\subsection
{
Theory Classification
}
\label
{
sec:classifier
}
``Semantic Search''  a very suggestive term, which is alas seriously underdefined 
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:theoryclassificationex
}
\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 wellknown 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
$
subsetclosed:
$
\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:theoryclassificationex
}
\end{figure}
\section
{
Conclusion
}
\label
{
sec:concl
}
\subsubsection*
{
Acknowledgements
}
The authors gratefully acknowledge financial support from the OpenDreamKit Horizon 2020
European Research Infrastructures project (
\#
676541) and the DFGfunded projec OAF: An
European Research Infrastructures project (
\#
676541) and the DFGfunded projec
t
OAF: An
Open Archive for Formalizations (KO 2428/131).
\renewcommand*
{
\bibfont
}{
\small
}
...
...
@@ 89,4 +165,7 @@ Open Archive for Formalizations (KO 2428/131).
% LocalWords: inst maketitle formalization defs wellformedness textsf sec:impl impl
% LocalWords: sec:conc conc Universit printbibliography ednote Internalizing newpage
% LocalWords: ifshort sec:relwork relwork renewcommand bibfont
% LocalWords: ifshort sec:relwork relwork renewcommand bibfont tbw setcounter tocdepth
% LocalWords: tableofcontents defemph compactenum emptyset newpart compactitem lstset
% LocalWords: centering aboveskip 0pt,belowskip hline lstlisting mathescape rightarrow
% LocalWords: vdash baseset sec:concl subsubsection Formalizations
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