forked from Isabelle_DOF/Isabelle_DOF
611 lines
19 KiB
TeX
611 lines
19 KiB
TeX
\RequirePackage{ifvtex}
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\documentclass[25pt, a0paper, portrait]{tikzposter}
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\usepackage[T1]{fontenc}
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\usepackage[utf8]{inputenc}
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\usepackage[T1]{fontenc}
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\usepackage[utf8]{inputenc}
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\usepackage{textcomp}
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\bibliographystyle{abbrvnat}
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\usepackage[english]{babel}
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\RequirePackage[caption]{subfig}
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\usepackage{isabelle}
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\usepackage{isabellesym}
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\IfFileExists{DOF-core.sty}{}{%
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\PackageError{DOF-core}{Isabelle/DOF not installed.
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This is a Isabelle_DOF project. The document preparation requires
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the Isabelle_DOF component from:
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<isadofurl>
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}{For further help, see <isadofurl>}
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}
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\input{ontologies}
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\IfFileExists{preamble.tex}{\input{preamble.tex}}{}%
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\usepackage{amsmath}
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\usepackage{DOF-amssymb}
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\usepackage[numbers, sort&compress, sectionbib]{natbib}
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\usepackage{graphicx}
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\usepackage{hyperref}
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\setcounter{tocdepth}{3}
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\hypersetup{%
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bookmarksdepth=3
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,pdfpagelabels
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,pageanchor=true
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,bookmarksnumbered
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,plainpages=false
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} % more detailed digital TOC (aka bookmarks)
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\sloppy
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\allowdisplaybreaks[4]
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\urlstyle{rm}
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\isabellestyle{it}
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\newenvironment{frontmatter}{}{}
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\title{%
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\parbox{\linewidth}{%
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\centering Isabelle/DOF:\\
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A Framework for Proving Ontology-Relations
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and Runtime Testing Ontology Instances%
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}}
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\author{Idir Ait-Sadoune, Nicolas Méric and Burkhart Wolff}
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\date{\today}
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\institute{Université Paris-Saclay, LMF, France}
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\usepackage{blindtext}
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\usepackage{comment}
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\usepackage{amsmath}
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% Process bibliography using biber engine.
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%\usepackage[
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% biber, the default backend of biblatex, supports Ascii,
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% 8-bit encodings, utf-8, on-the-fly reencoding, locale-specific sorting,
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% and many other features.
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% Locale-specific sorting, case-sensitive sorting,
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% and upper/lowercase precedence are controlled by the options
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% sortlocale, sortcase, and sortupper, respectively.
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% See biblatex documentation file biblatex.pdf,
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% 3.12, 2018/10/30, section 3.1.1, page 45.
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% backend=biber,
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% Whether or not to print back references in the bibliography.
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% The back references are a list of page numbers indicating the pages
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% on which the respective bibliography entry is cited.
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% If there are refsection environments in the document,
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% the back references are local to the reference sections.
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% Strictly speaking, this option only controls
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% whether the biblatex package collects the data required
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% to print such references.
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% This feature still has to be supported by the selected bibliography style.
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% All standard styles which come with this package do so.
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% See biblatex documentation file biblatex.pdf,
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% 3.12, 2018/10/30, section 3.1.2.1, page 50.
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% backref=true,
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% Loads the citation style <file>.cbx.
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% See § 3.3.1 for an overview of the standard citation styles.
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% See biblatex documentation file biblatex.pdf,
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% 3.12, 2018/10/30, section 3.1.1, page 45.
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% citestyle=alphabetic,
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% Loads the bibliography style <file>.bbx.
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% See § 3.3.2 for an overview of the standard bibliography styles.
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% See biblatex documentation file biblatex.pdf,
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% 3.12, 2018/10/30, section 3.1.1, page 45.
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% bibstyle=alphabetic,
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%]{biblatex}
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\usetheme{Simple}
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% Add bibliography using biblatex macro.
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%
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% Adds a <resource>, such as a .bib file, to the default resource list.
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% This command is only available in the preamble.
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% It replaces the \bibliography legacy command.
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% Note that files must be specified with their full name,
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% including the extension.
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% Do not omit the .bib extension from the filename.
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% Also note that the <resource> is a single resource.
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% If the resources contain duplicate entries (that is, duplicate entrykeys),
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% it is backend dependent what then happens.
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% For example, by default biber will ignore
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% further occurrence of entrykeys unless its --noskipduplicates options is
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% used.
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% Invoke \addbibresource multiple times to add more resources.
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% See biblatex documentation file biblatex.pdf,
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% 3.12, 2018/10/30, section 3.7.1, page 81-82.
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%\addbibresource{bibliography.bib}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\def\HyperFirstAtBeginDocument#1{#1}
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\begin{document}
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\begin{frontmatter}
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\maketitle
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% \tableofcontents
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\end{frontmatter}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{columns}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\column{0.33}
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% \block{Overview}{
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% \begin{itemize}
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% \item
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% Why (Document) Ontologies
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% \item
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% Ontologies and Formal Theories
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% \item
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% DOF Design
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% \item
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% Isabelle/DOF Implementation
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% \item
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% Some Application Scenarios
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% \end{itemize}
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% TODO: Add figure
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% PUBLIC RELEASE:
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% http/10.5281/zenodo.3370483
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% }
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\block{Linking the Formal and the Informal: Why Ontologies?}{
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% \begin{itemize}
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% \item
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% More powerful ITP systems
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% \(\Longrightarrow\) body of formalised mathematics and engineering
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% \item
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The Isabelle Archive Formal of Proof as example :
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\begin{tikzfigure}
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\includegraphics[width=0.4\linewidth]{%
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figures/afp_growth_in_number_of_articles.png}
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\end{tikzfigure}
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In 2022, the count stood at 661
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articles, 420 authors and 3.3 M loc !
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% \item
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}
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Problem of logical consistency technically solved via continuous proof-checking
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Problem of knowledge retrieval and of linking semi-formal explanations to
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definitions and proofs still largely open.
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The central role in technologies adressing the \emph{knowledge} problem
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is played by \emph{document ontologies}, i.e., a machine-readable form
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of meta-data attached to document-elements as well as their document discourse.
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In order
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to make these techniques applicable to \emph{formal theory development},
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the following is needed:
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\begin{itemize}
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\item
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a general mechanism to define and develop \emph{domain-specific} ontologies,
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\item
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... that should be adapted to entities occurring in formal theories,
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i.e., provide built-in support for types, terms, theorems, proofs, etc.,
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\item
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ways to annotate meta-data generated by ontologies to the document elements,
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as ``deep'' as possible, together with strong validation checks,
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\item
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a smooth integration into the theory document development process, and
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\item
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ways to relate ontologies and ontology-conform documents along different
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ontologies by \emph{ontological mappings} and \emph{data translations}
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\footnote{We follow throughout this text the terminology established in
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\cite{books/daglib/0032976}, pp. 39 ff.}
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\end{itemize}
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% Rising need for:
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% % \begin{itemize}
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% % \item
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% structuring and consistency,
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% % \item
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% advanced “semantic” search,
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% % \item
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% tool-interaction.
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% % \end{itemize}
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% % \end{itemize}
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% % \begin{itemize}
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% % \item
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% This requires more structured and typed meta-information
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% % for our application domain
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% in theory developments
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% % \item
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% and a better dependency-control of the different document elements,
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% like
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% % \begin{itemize}
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% % \item
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% types, terms, theorems
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% % \item
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% code % (proof-terms, proof generating programs, SML, LaTeX etc, but also Scala and C! )
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% % \item
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% text and diagrams %(and perhaps animations, see Jupyter Notebooks https://jupyter.org/ )
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% % \item
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% … and the links between them, requiring notions of
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% consistency and coherence for collaborative development
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% % \end{itemize}
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% % \item
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% The language in which such meta-information can be specified
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% is called a \emph{document ontology} %(or \emph{vocabulary})
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% % \end{itemize}
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}
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% \block{Linking the Formal and the Informal\\ - Existing Approaches -}{
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% \begin{itemize}
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% \item
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% Code Antiquotations as in LISP, MetaML, SML, …
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% \begin{tikzfigure}
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% \includegraphics[width=0.4\linewidth]{%
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% figures/code_antiquotations.png}
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% \end{tikzfigure}
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% \item
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% Document pragmas as in JavaDoc, Doxygen, et al
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% TODO: Add figure
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% \item
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% Compilation process allows for document generation and some consistency checks
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% \(\Longrightarrow\) batch mode consistency only.
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% \item
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% The Isabelle Approach to “Text-Antiquotations”
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% (heavily used to assure \emph{coherence} and
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% \emph{traceability} in the technical documentations and papers)
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% \item
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% Definitions and proofs can be mixed with text elements
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% \begin{tikzfigure}
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% \includegraphics[width=0.4\linewidth]{%
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% figures/text_element.png}
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% \end{tikzfigure}
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% \item
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% Text Elements may contain Antiquotations to Formal Content
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% in the Logical Context, which are checked and animated in the IDE:
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% \begin{tikzfigure}
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% \includegraphics[width=0.4\linewidth]{%
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% figures/text_element_with_formal_content.png}
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% \end{tikzfigure}
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% \item
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% The global doc-generation process yields a presentation in, e.g., .pdf :
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% \begin{tikzfigure}
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% \includegraphics[width=0.4\linewidth]{%
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% figures/output.png}
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% \end{tikzfigure}
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% \item
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% Similarly, Isabelle Code uses heavily “SML-Antiquotations”
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% \item
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% SML System Code can be mixed with antiquotations producing
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% SML level representation of types and terms:
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% \begin{tikzfigure}
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% \includegraphics[width=0.4\linewidth]{%
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% figures/sml_code_with_antiquotations.png}
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% \end{tikzfigure}
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% \end{itemize}
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% }
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% \column{0.33}
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% \block{Isabelle's Document-Centric View on Formal Development}{
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% \begin{itemize}
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% \item
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% Primary document type: “XXX.thy”
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% \begin{tikzfigure}
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% \includegraphics[width=0.4\linewidth]{%
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% figures/theories_hierarchy.png}
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% \end{tikzfigure}
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% \begin{itemize}
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% \item
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% Acyclic Graph of units that consist of
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% a sequence of \emph{document elements}
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% called “commands”
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% \item
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% commands user-programmable in SML
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% \item
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% Support of Cascade Syntax:
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% @{SML ‹ … @{type ‹ …. ›} … ›}
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% \item
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% Commands are semantically transformers
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% of the logical context : \(\Theta \Rightarrow \Theta\)
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% \item
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% anti-quotations are “semantic macros” and as such partial) functions:
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% \(\Theta \Rightarrow \text{text}\)
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% \(\Theta \Rightarrow \text{sml}\)
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% \(\Theta \Rightarrow \text{term}\)
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% \item
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% pervasive continuous build/check of Isabelle/PIDE supports anti-quotations.
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% \end{itemize}
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% \end{itemize}
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% }
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\block{Isabelle/DOF}{
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\begin{itemize}
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\item
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DOF : The Document Ontology Framework
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has been designed as an Isabelle component that attempts to answer these needs.
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\item
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Prior Versions of Isabelle/DOF support semantic annotations of text and code-contexts:
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\(
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text*[label::classid, attr1 =E1 , ... attrn =En ]⟨ some semi-formal text ⟩
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\)
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\(
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ML*[label::classid, attr1 =E1 , ... attrn =En ] ⟨ some SML code ⟩
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\)
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TODO: Add figure
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\item
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Novelty in Isabelle/DOF: support of \(\lambda\)-term-contexts, e.g.:
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\(value*[label::classid, attr1 =E1 , ... attrn =En ]⟨ some annotated \lambda-term ⟩\)
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TODO: Add figure
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formal, machine-checked invariants on meta-data, which correspond to the concept of
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``rules'' in OWL~ \cite{OWL2014} or ``constraints'' in UML, and which can be specified in
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common Isabelle/HOL \(\lambda\)-term syntax.
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\end{itemize}
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% \innerblock{Isabelle/DOF}{
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% AAAAAAAAAAAAAAAAAAAAAAAAAAAAA
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% }
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}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\column{0.33}
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\block{Isabelle/DOF Core : ODL}{
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\begin{itemize}
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\item
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The Ontology Definition Language (ODL):
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The Mechanism to \emph{define} Ontologies
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\item
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Features:
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\begin{tikzfigure}
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\includegraphics[width=0.4\linewidth]{%
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figures/odl.png}
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\end{tikzfigure}
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\begin{itemize}
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\item
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classes (for the “concepts”)
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\item
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classes may have attributes
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with HOL type
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\item
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class declarations can be
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interleaved with arbitrary HOL
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declarations
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\item
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attributes of class-instances
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are mutable; (default) values
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can be denoted by HOL-terms
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\item
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class declarations induce a HOL-type;
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this allows to establish “ontological links”
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\end{itemize}
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\begin{tikzfigure}
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\includegraphics[width=0.4\linewidth]{%
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figures/dof_classes.png}
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\end{tikzfigure}
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\begin{itemize}
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\item
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classes have single inheritance
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(is a - relation)
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\item
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attribute overriding of attributes is possible
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\item
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meta-level types of the ITP were included as abstract HOL types;
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their inhabitance is checked
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in the global context \(\theta\)
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\end{itemize}
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\end{itemize}
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}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% \column{0.33}
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\block{DOF Example Document}{
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\begin{itemize}
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\item
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Defining the Ontological Context
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\begin{tikzfigure}
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\includegraphics[width=0.4\linewidth]{%
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figures/ontological_context.png}
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\end{tikzfigure}
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\item
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And there we go:
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\begin{tikzfigure}
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\includegraphics[width=0.4\linewidth]{%
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figures/dof_document.png}
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\end{tikzfigure}
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\item
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… where title* and
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abstract* are macros
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for text*[a::title,…],
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etc…
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\item
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… and the meta-data
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instances are a, abs,
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intro, T1, attached to
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these doc elements …
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\end{itemize}
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}
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\block{Isabelle/DOF Core : Class Invariants}{
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\begin{itemize}
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\item
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ODL used already \(\lambda\)-(ground)-terms to denote values for attributes.
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\item
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New: ODL uses arbitrary \(\lambda\)-terms containing generated
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\emph{term-antiquotations in invariants},
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attribute definitions and commands like value*
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\item
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Eg.: Invariants for
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\begin{tikzfigure}
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\includegraphics[width=0.4\linewidth]{%
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figures/classes_with_invariant.png}
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\end{tikzfigure}
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TODO: FIGURE MUST BU UPDATED!!! See original example
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\begin{itemize}
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\item
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data-integrity constraints
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\item
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… using “built-in” term antiquotations for “term”, “typ”, “thm”
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\item
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may use DOF-generated term-antiquotations
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like @{result ‘’<some result instance>’’}
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or @{introduction ‘’intro’’} or @{instance-of ‘’result’’}, etc.
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\item
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“a result text element must provide evidence
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in form of a proven theorem …”
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\end{itemize}
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\end{itemize}
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}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\column{0.33}
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\block{Consequences}{
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\begin{itemize}
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\item
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If an ODL ontology generates “intra-logical” representations,
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what’s the benefit ?
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\begin{itemize}
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\item
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We don't have to learn a new (meta)-language
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\item
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We can define new operations on them inside
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the logic and develop their theory …
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\item
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… to develop a query language, for example:
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\(
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value*⟨ filter (is_interesting) @\{instances-of "result"\} ⟩
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\)
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\item
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We can relate ontologies and ontology instances
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by formal proof (‘’ontology alignment, ontology mapping’’)
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\end{itemize}
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\end{itemize}
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}
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\block{Consequences: Example Proof of an Ontology Mapping}{
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\begin{itemize}
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\item
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A “‘Generic’ Reference Ontology” vs. a “‘local’ Ontology”
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\begin{tikzfigure}
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\includegraphics[width=0.4\linewidth]{%
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figures/reference_ontology.png}
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\end{tikzfigure}
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\begin{tikzfigure}
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\includegraphics[width=0.4\linewidth]{%
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figures/local_ontology.png}
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\end{tikzfigure}
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\begin{tikzfigure}
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\includegraphics[width=0.4\linewidth]{%
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figures/morphism.png}
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\end{tikzfigure}
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\item
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“The mapping is correct (preserves the invariants)”
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\begin{tikzfigure}
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\includegraphics[width=0.4\linewidth]{%
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figures/invariant_preserved.png}
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\end{tikzfigure}
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\end{itemize}
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}
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\block{But what “are” ontology-generated term antiquotations ???}{
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\begin{itemize}
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\item
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First of all: how are they processed:
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\begin{itemize}
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\item parsing
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\item type checking
|
||
\item validation (an argument is indeed a valid reference in the context)
|
||
\item expansion (replacement of a reference against logical terms)
|
||
\item evaluation (to SML code, or by nbe)
|
||
\end{itemize}
|
||
\item
|
||
Then “built-in” term-anti quotations can be:
|
||
\begin{itemize}
|
||
\item
|
||
just uninterpreted constants (without expansion)
|
||
TODO: Add figure
|
||
\item
|
||
a ‘’shallow’’ data-type representation (without expansion)
|
||
TODO: Add figure
|
||
\item
|
||
or a “deep” data-type representation into an Isabelle
|
||
Meta-Model such as [Nipkow,Rosskopf 21] (with expansion)
|
||
TODO: Add figure
|
||
\end{itemize}
|
||
\end{itemize}
|
||
}
|
||
|
||
\block{Conclusion}{
|
||
\begin{itemize}
|
||
\item
|
||
DOF provides a framework
|
||
\begin{itemize}
|
||
\item
|
||
for defining ontologies in the context of ITP systems
|
||
\item
|
||
its typed ! It has a logical interpretation !
|
||
\item
|
||
provides a generated infrastructure for meta-data of
|
||
types, terms, thm’s and text and code elements
|
||
\end{itemize}
|
||
\item
|
||
DOF provides a framework to enforce on-the-fly
|
||
ontology-conform documentation checking
|
||
\item
|
||
DOF provides infrastructure for proofs over the
|
||
logical representation of ontologies and meta-data …
|
||
\item
|
||
Ontologies generating meta-data can be used
|
||
for other forms of Tool Interaction via “deep
|
||
interpretations” into a meta-model
|
||
\item
|
||
(P)IDE's are more than just a technical asset
|
||
\item
|
||
… it is a corner-stone for a revolution
|
||
\begin{itemize}
|
||
\item
|
||
1970’ies TEXT
|
||
\item
|
||
1990’ies HYPERTEXT
|
||
\item
|
||
2010’ies REACTIVE DOCUMENTS
|
||
\item
|
||
2020’ies SEMANTIC DOCUMENTS (???)
|
||
\end{itemize}
|
||
\end{itemize}
|
||
}
|
||
|
||
\end{columns}
|
||
|
||
\input{session}
|
||
|
||
\block{References}{
|
||
% optional bibliography
|
||
\IfFileExists{root.bib}{{\bibliography{root}}}{}
|
||
\end{document}
|
||
%\printbibliography
|
||
}
|
||
|
||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
% \begin{columns}
|
||
% \column{0.4}
|
||
% \block{More text}{Text and more text}
|
||
|
||
% \column{0.6}
|
||
% \block{Something else}{Here, \blindtext \vspace{4cm}}
|
||
% \note[
|
||
% targetoffsetx=-9cm,
|
||
% targetoffsety=-6.5cm,
|
||
% width=0.5\linewidth
|
||
% ]
|
||
% {e-mail \texttt{welcome@overleaf.com}}
|
||
% \end{columns}
|
||
|
||
% \begin{columns}
|
||
% \column{0.5}
|
||
% \block{A figure}
|
||
% {
|
||
% \begin{tikzfigure}
|
||
% % \includegraphics[width=0.4\textwidth]{images/overleaf-logo}
|
||
% \end{tikzfigure}
|
||
% }
|
||
% \column{0.5}
|
||
% \block{Description of the figure}{\blindtext}
|
||
% \end{columns}
|
||
|
||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
\end{document}
|
||
|