Revise related works, first pass
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- Shorten mathematical aspects - Introduce AFP
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@ -1237,39 +1237,37 @@ subsection*[rw::related_work]\<open>Related Work\<close>
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text\<open>There are a number of approaches to use ontologies for structuring the link between
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text\<open>There are a number of approaches to use ontologies for structuring the link between
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information and knowledge, and to make it amenable to
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information and knowledge, and to make it amenable to
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``semantic'' search in or consistency checking of documents:
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``semantic'' search in or consistency checking of documents.
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Some are targeting mathematical libraries:
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\<^item> The search engine \<^url>\<open>http://shinh.org/wfs\<close> uses a quite brute-force,
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\<^item> The search engine \<^url>\<open>http://shinh.org/wfs\<close> uses clever text-based search methods in
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but practical approach. It is getting its raw-data from Wikipedia and PlanetMath
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and similar sites, and uses clever text-based search methods in
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a large number of formulas, agnostic of their logical context, and of formal proof.
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a large number of formulas, agnostic of their logical context, and of formal proof.
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\<^item> The OAF project @{cite "KohlhaseR21"} comes closest to our ideal of wide-spread
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\<^item> The OAF project @{cite "KohlhaseR21"}
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use of ontologies for search in mathematical libraries.
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developed a common ontological format, called OMDoc/MMT, and
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The project developed a common ontological format, called OMDoc/MMT, and
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developed six \<^emph>\<open>export\<close> functions from major ITP systems into it.
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developed six \<^emph>\<open>export\<close> functions from major ITP systems into it. The more difficult task to
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The emphasis was put on building
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develop \<^emph>\<open>import\<close> functions has not been addressed, not to mention the construction
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of imported proofs in a native tactic proof format. Rather, the emphasis was put on building
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a server infrastructure based on conventional, rather heavy-weight database and OWL technology.
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a server infrastructure based on conventional, rather heavy-weight database and OWL technology.
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Our approach targets so far only one ITP system and its libraries, and emphasizes
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type-safeness, expressive power and ``depth'' of meta-data, which is adapted
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to the specific needs of ITP systems and theory developments.
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\<^item> There are meanwhile a number of proposals of ontologies targeting mathematics:
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\<^item> There are meanwhile a number of proposals of ontologies targeting mathematics:
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\<^item> OntoMath\textsuperscript{PRO} @{cite "Nevzorova2014OntoMathPO"} proposes a
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\<^item> OntoMath\textsuperscript{PRO} @{cite "Nevzorova2014OntoMathPO"} proposes a
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``taxonomy of the fields of mathematics'' (pp 110). In total,
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``taxonomy of the fields of mathematics'' (pp 110). In total,
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OntoMath\textsuperscript{PRO} contains the daunting number of 3,449 classes, which is in part due to
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OntoMath\textsuperscript{PRO} contains the daunting number of 3,449 classes,
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which is in part due to
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the need to compensate the lack of general datatype definition methods for meta-data.
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the need to compensate the lack of general datatype definition methods for meta-data.
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It is inspired from a translation of the Russian Federal Standard for Higher Education
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on mathematics for master students,
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which makes it nevertheless an interesting starting point for a future development
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of a mathematics ontology in the \<^dof> framework.
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\<^item> Other ontologies worth mentioning are DBpedia @{cite "10.1007/978-3-540-76298-0_52"},
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\<^item> Other ontologies worth mentioning are DBpedia @{cite "10.1007/978-3-540-76298-0_52"},
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which provides with the \<^emph>\<open>SPARQL endpoint\<close> \<^url>\<open>http://dbpedia.org/sparql\<close> a search engine,
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which provides with the \<^emph>\<open>SPARQL endpoint\<close> \<^url>\<open>http://dbpedia.org/sparql\<close> a search engine,
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and the more general ScienceWISE \<^footnote>\<open>\<^url>\<open>http://sciencewise.info/ontology/\<close>.\<close>
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and the more general ScienceWISE \<^footnote>\<open>\<^url>\<open>http://sciencewise.info/ontology/\<close>.\<close>
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that allows users to introduce their own category concepts.
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that allows users to introduce their own category concepts.
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Both suffer from the lack of deeper meta-data modeling, and the latter is still at the beginning
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(ScienceWISE marks the Mathematics part as ``under construction'').
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Our approach emphasizes type-safeness, expressive power and ``depth'' of meta-data,
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which is adapted to the specific needs of ITP systems and theory developments.
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It is a concrete proposal for the ITP community allowing
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a deeper structuring of mathematical libraries
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such as the Isabelle Archive of Formal Proofs (AFP)~@{cite "AFP-ref22"}
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which passed the impressive numbers of 650 articles,
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written by 420 authors at the beginning of 2022.
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% \<^url>\<open>https://github.com/CLLKazan/OntoMathPro\<close>
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% \<^url>\<open>https://github.com/CLLKazan/OntoMathPro\<close>
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%
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