Add back position in mathematical oriented related works
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Nicolas Méric 2022-04-22 14:56:39 +02:00
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@ -1133,23 +1133,30 @@ information and knowledge, and to make it amenable to
``semantic'' search in or consistency checking of documents. ``semantic'' search in or consistency checking of documents.
Some are targeting mathematical libraries, Some are targeting mathematical libraries,
like the search engine \<^url>\<open>http://shinh.org/wfs\<close> which uses clever text-based search methods in like the search engine \<^url>\<open>http://shinh.org/wfs\<close> which uses clever text-based search methods in
a large number of formulas, agnostic of their logical context and of formal proof, a large number of formulas, agnostic of their logical context and of formal proof,
or the OAF project @{cite "KohlhaseR21"} which or the OAF project @{cite "KohlhaseR21"} which developed a common ontological format,
developed a common ontological format, called OMDoc/MMT, and called OMDoc/MMT, and six \<^emph>\<open>export\<close> functions from major ITP systems into it.
six \<^emph>\<open>export\<close> functions from major ITP systems into it. The more difficult task to develop import functions has not been addressed, not to mention
The emphasis was put on building the construction of imported proofs in a native tactic proof format. Rather, the emphasis
a server infrastructure based on conventional, rather heavy-weight database and OWL technology. was put on building a server infrastructure based on conventional, rather heavy-weight
database and OWL technology. Our approach targets so far only one ITP system and
its libraries, and emphasizes type-safeness, expressive power and “depth” of meta-data,
which is adapted to the specific needs of ITP systems and theory developments.
There are also a number of proposals of ontologies targeting mathematics: There are also a number of proposals of ontologies targeting mathematics:
the OntoMath\textsuperscript{PRO} @{cite "Nevzorova2014OntoMathPO"} proposes a the OntoMath\textsuperscript{PRO} @{cite "Nevzorova2014OntoMathPO"} proposes a
``taxonomy of the fields of mathematics'' (pp 110). In total, ``taxonomy of the fields of mathematics'' (p. 6).
OntoMath\textsuperscript{PRO} contains the daunting number of 3,449 classes, In total, OntoMath\textsuperscript{PRO} contains the daunting number of 3,449 classes,
which is in part due to which is in part due to the need to compensate
the need to compensate the lack of general datatype definition methods for meta-data. the lack of general datatype definition methods for meta-data.
It is nevertheless an interesting starting point for a future development of a mathematics ontology
in the \<^dof> framework.
Other ontologies worth mentioning are DBpedia @{cite "10.1007/978-3-540-76298-0_52"}, Other ontologies worth mentioning are DBpedia @{cite "10.1007/978-3-540-76298-0_52"},
which provides with the \<^emph>\<open>SPARQL endpoint\<close> \<^url>\<open>http://dbpedia.org/sparql\<close> a search engine, which provides with the \<^emph>\<open>SPARQL endpoint\<close> \<^url>\<open>http://dbpedia.org/sparql\<close> a search engine,
and the more general ScienceWISE \<^footnote>\<open>\<^url>\<open>http://sciencewise.info/ontology/\<close>.\<close> and the more general ScienceWISE \<^footnote>\<open>\<^url>\<open>http://sciencewise.info/ontology/\<close>.\<close>
that allows users to introduce their own category concepts. that allows users to introduce their own category concepts.
Both suffer from the lack of deeper meta-data modeling, and the latter is still at the beginning
(ScienceWISE marks the Mathematics part as ``under construction'').
Regarding using formal methods to formalise standards, Event-B method was used by Regarding using formal methods to formalise standards, Event-B method was used by
Fotso et al. @{cite "FotsoFLM18"} to propose a specification of the hybrid ERTMS/ETCS level 3 standard, Fotso et al. @{cite "FotsoFLM18"} to propose a specification of the hybrid ERTMS/ETCS level 3 standard,