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Burkhart Wolff 2022-04-19 19:59:26 +02:00
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@ -135,15 +135,15 @@ Still, while the problem of logical consistency
even under system-changes and pervasive theory evolution is technically solved via continuous
proof-checking, the problem of knowledge retrieval and of linking semi-formal explanations to
definitions and proofs remains largely open.
The \<^emph>\<open>knowledge\<close> problem of the increasingly massive \<^emph>\<open>digital information\<close> available
incites numerous research efforts summarized under the labels ``semantic web'',
``integrated document management'', or any form of advanced ``semantic'' text processing.
These technologies are increasingly important in jurisprudence, medical research and
life-sciences in order to tame their respective publication tsunamies. The central role
in these technologies is played by \<^emph>\<open>document ontologies\<close>, \<^ie>, a machine-readable form
% The \<^emph>\<open>knowledge\<close> problem of the increasingly massive \<^emph>\<open>digital information\<close> available
% incites numerous research efforts summarized under the labels ``semantic web'',
% ``integrated document management'', or any form of advanced ``semantic'' text processing.
% These technologies are increasingly important in jurisprudence, medical research and
% life-sciences in order to tame their respective publication tsunamies.
The central role in technologies adressing the \<^emph>\<open>knowledge\<close> problem
is played by \<^emph>\<open>document ontologies\<close>, \<^ie>, a machine-readable form
of meta-data attached to document-elements as well as their document discourse. In order
to make these techniques applicable to the area of \<^emph>\<open>formal theory development\<close>,
to make these techniques applicable to \<^emph>\<open>formal theory development\<close> ,
the following is needed: \<^vs>\<open>0.2cm\<close>
\<^item> a general mechanism to define and develop \<^emph>\<open>domain-specific\<close> ontologies,
@ -171,7 +171,7 @@ proofs, text-elements, etc., prevailing in the Isabelle system framework.
In more detail, \<^dof> introduces a number of ``ontology aware'' text-elements with analogous
syntax to standard ones. The difference is a bracket with meta-data of the form:
@{theory_text [display,indent=5, margin=70]
@{theory_text [display,indent=10, margin=70]
\<open>text*[label::classid, attr\<^sub>1=E\<^sub>1, ... attr\<^sub>n=E\<^sub>n]\<open> some semi-formal text \<close>
ML*[label::classid, attr\<^sub>1=E\<^sub>1, ... attr\<^sub>n=E\<^sub>n]\<open> some SML code \<close>
...\<close>}
@ -188,13 +188,13 @@ called \<^emph>\<open>antiquotation\<close> that depends on the logical context
With standard Isabelle antiquotations, for example, the following text element
of the integrated source will appear in Isabelle/PIDE as follows:
@{theory_text [display,indent=5, margin=70]
@{theory_text [display,indent=10, margin=70]
\<open>text\<open> According to the reflexivity axiom @{thm refl}, we obtain in \<Gamma>
for @{term "fac 5"} the result @{value "fac 5"}.\<close>\<close>}
for @{term "fac 5"} the result @{value "fac 5"}.\<close>\<close>}
In the corresponding generated \<^LaTeX> or HTML output, this looks like this:
@{theory_text [display,indent=5, margin=70]
\<open>According to the reflexivity axiom \<open>x = x\<close>,
we obtain in \<Gamma> for \<open>fac 5\<close> the result \<open>120\<close>.\<close>}
@{cartouche [display,indent=17, margin=70]
\<open>According to the reflexivity axiom \<open>x = x\<close>, we obtain in \<Gamma>
for \<open>fac 5\<close> the result \<open>120\<close>.\<close>}
where the meta-texts \<open>@{thm refl}\<close> (``give the presentation of theorem `refl'\,\!''),
\<open>@{term "fac 5"}\<close> (``parse and type-check `fac 5' in the previous logical context'')
and \<open>@{value "fac 5"}\<close> (``compile and execute `fac 5' according to its
@ -239,25 +239,24 @@ text\<open>As novel contribution, this work extends prior versions of \<^dof> by
``rules'' in OWL~ @{cite "OWL2014"} or ``constraints'' in UML, and which can be specified in
common \<^hol> \<open>\<lambda>\<close>-term syntax.
\<close>
text\<open> For example, the \<^dof> evaluation command taking a \<^hol>-expression:
@{theory_text [display,indent=5, margin=70]
\<open>value*[ass::Assertion, relvce=2::int]
\<open>filter (\<lambda> \<sigma>. relvce \<sigma> > 2) @{Assertion-instances}\<close>\<close>}
text\<open> \<^noindent> For example, the \<^dof> command evaluating the \<^hol>-expression:
@{theory_text [display,indent=10, margin=70]
\<open>value*[ass::Assertion, relvce=4::int]
\<open>filter (\<lambda> \<sigma>. relvce \<sigma> > 2) @{Assertion-instances}\<close>\<close>}
where \<^dof> command \<open>value*\<close> type-checks, expands in an own validation phase
the \<open>Assertion-instances\<close>-term antiquotation, and evaluates the resulting \<^hol> expression
above. Assuming an ontology providing the class \<open>Assertion\<close> having at least the
integer attribute \<open>relvce\<close>, the command finally creates an instance of \<open>Assertion\<close> and
binds this to the label \<open>ass\<close> for further use.
binds this to label \<open>ass\<close>, while setting its \<open>relvce\<close> to 4.
Beyond the gain of expressivity in \<^dof> ontologies, term-antiquotations pave the way
Beyond the gain of expressivity in \<^dof> ontologies, term-anti\-quotations pave the way
for advanced queries of elements inside an integrated source, and invariants
allow for formal proofs over the relations/translations of ontologies and ontology-instances.
The latter question raised scientific interest under the label ``ontology mapping'' for
which we therefore present a formal solution. To sum up, we completed \<^dof> to
a fairly rich, ITP-oriented ontology language, which is a concrete proposal for the
ITP community allowing a deeper structuring of mathematical libraries
such as the Archive of Formal Proofs (AFP).
\<close>
such as the AFP.\<close>
(*<*)
declare_reference*[casestudy::text_section]