=Paper=
{{Paper
|id=Vol-2022/paper50
|storemode=property
|title=
Lobachevskii DML: Towards a Semantic Digital Mathematical Library of Kazan University
|pdfUrl=https://ceur-ws.org/Vol-2022/paper50.pdf
|volume=Vol-2022
|authors=Alexander M. Elizarov,Evgeny K. Lipachev
|dblpUrl=https://dblp.org/rec/conf/rcdl/ElizarovL17
}}
==
Lobachevskii DML: Towards a Semantic Digital Mathematical Library of Kazan University
==
https://ceur-ws.org/Vol-2022/paper50.pdf
Lobachevskii DML: Towards a Semantic Digital
Mathematical Library of Kazan University
© Alexander M. Elizarov © Evgeny K. Lipachev
N. I. Lobachevskii Institute of Mathematics and Mechanics,
Kazan (Volga Region) Federal University,
Kazan, Russia
amelizarov@gmail.com elipachev@gmail.com
Abstract. The digital mathematical library Lobachevskii DML is one of the national initiatives that
have emerged in the past decade in different countries of the world. During this time, the formed technical
and organizational conditions allowed making mathematicians’ dreams of a global World Digital Mathemat-
ical Library (WDML) a reality. Following the vision approved by the International Mathematical Union, we
started the Lobachevskii DML project in 2017 – the year of the 225-th anniversary of the birth of the bril-
liant mathematician Nikolai Ivanovich Lobachevskii, the founder of non-Euclidean geometry, the rector of
the Kazan University. The main task of Lobachevskii DML project is the development of tools for manag-
ing mathematical content, which take into account not only the specifics of mathematical texts, but also the
features of processing Russian-language texts. A particular task of creating this digital library is the integra-
tion of mathematical resources of Kazan University. Therefore, the original goal of the project was to build
up a sound basis for a digital archive comprising the relevant mathematical literature published for 213
years of the existence of Kazan University and stored in the libraries of the University and Kazan. Accord-
ing to our assumption, the digital library Lobachevskii DML should be endowed with all conceivable neces-
sary functions and services, making it a comprehensive and up-to-date live DML, generally respected and
used by the local as well as the global mathematical community. From the very beginning, we had in mind
that the Lobachevskii DML should constitute a building block for the envisioned global WDML.
In this paper, the results of the implementation of the digital mathematical library Lobachevsky-DML
are presented. We describe the purpose of creating this digital library, methods of managing mathematical
content based on semantic technologies. The following show how Lobachevskii DML interacts with the in-
formation systems of scientific journals. We also present a system of services to support the life cycle of a
mathematical document and highlight technologies for supporting new forms of scientific publications and
providing integration services with other digital mathematical archives and libraries.
Keywords: semantic technologies, semantic publishing, digital mathematics library, DML, World
Digital Mathematics Library (WDML) project, Lobachevskii DML
skii DML, http://www.Lobachevskii-dml.ru/), which we
Introduction develop in accordance with the basic principles of
The creation and development of specialized digital WDML. The digital mathematical library Lobachevskii
libraries (DL) are one of the directions for the formation DML is another of the national initiatives that have
of a global scientific infrastructure. In the field of math- emerged in the past decade in different countries of the
ematics, the problems of integrating knowledge ob- world. During this time, the formed technical and organ-
tained over the entire “printed” period of the develop- izational conditions allowed making mathematicians’
ment of this science have been considered in a number dreams of a global WDML a reality. Following the vi-
of projects (see, for example, [1]). Even when such pro- sion approved by the International Mathematical Union,
jects were of a local nature, the methods and tools de- we started the Lobachevskii DML project in 2017 – the
veloped during their implementation were oriented to- year of the 225-th anniversary of the birth of the bril-
wards a comprehensive integration of knowledge (see, liant mathematician Nikolai Ivanovich Lobachevskii,
for example, [2–4]). the founder of non-Euclidean geometry, the rector (from
1827 to 1845) of the Kazan University. The year 2017
The modern vision of the tasks of forming a global
was announced at the Kazan University of as the “Year
infrastructure of mathematical knowledge is reflected in
of N. I. Lobachevskii”.
the documents of the World Digital Mathematics Li-
brary (WDML) project [5]. In these documents, it was The main task of Lobachevskii DML project is the
noted that the leading role in the formation of digital development of such tools for managing mathematical
mathematical collections, the accompaniment of their content, which take into account not only the specifics
metadata (annotations, key words, etc.) is given by the of mathematical texts, but also the features of pro-
“smaller” DML. cessing Russian-language texts. A particular task of
creating this digital library is the integration of mathe-
The present work is devoted to the presentation of
matical resources of Kazan University. Therefore, the
Lobachevskii Digital Mathematics Library (Lobachev-
326
original goal of the project was to build up a sound basis es and principles of their construction, as well as ser-
for a digital archive comprising the relevant mathemati- vices for managing scientific content is contained in
cal literature published for 213 years of the existence of [11]. Implementation and development of digital math-
Kazan University and stored in the libraries of the Uni- ematical libraries are associated with the development
versity and Kazan. According to our assumption, the of special tools and the continuous improvement of their
digital library Lobachevskii DML should be endowed functionality.
with all conceivable necessary functions and services, Since the beginning of the 21st century, a number of
making it a comprehensive and up-to-date live DML, developers have created information systems for the
generally respected and used by the local as well as the management of electronic scientific journals. We com-
global mathematical community. From the very begin- pared these systems according to the selected criteria
ning, we had in mind that the Lobachevskii DML [12]. As a result, the OJS system was recognized as the
should constitute a building block for the envisioned optimal [13]. We successfully implemented this infor-
global WDML. mation platform in the journals Lobachevskii Journal of
In this paper, the results of the development of the Mathematics (LJM, http://ljm.kpfu.ru/)/), one of the first
digital mathematical library Lobachevsky-DML are Russian electronic mathematical journals, and Russian
presented. We describe the purpose of creating this digi- Digital Libraries (http://ojs.kpfu.ru/index.php/elbib). To
tal library, methods of managing mathematical content manage digital content, we also developed a number of
based on semantic technologies. The following shows tools that automate a whole series of editorial processes.
how Lobachevskii DML interacts with the information These include, in particular, the choice of recommenda-
systems of scientific journals. We also present a system tions for the selection of reviewers, style validation of
of services to support the life cycle of a mathematical author's documents, search tools, article design services,
document and highlight technologies for supporting new etc. These tools served as the technological basis for the
forms of scientific publications and providing integra- Lobachevskii DML developed by us (see Section 3).
tion services with other digital mathematical archives Let us also pay attention to important results related
and libraries. to the formalization of the of mathematical articles rep-
1 Information Systems in Mathematics resentations. For these purposes, specialized formal
languages for the presentation of mathematical texts
Since inception of the first scientific information have been developed (see, for example, [14–18]). These
systems, the community of mathematicians has been technologies are also used to construct a mathematical
involved in the full cycle of developing such systems, ontology and create a semantic search service [19–22].
from basic idea to full-scale implementation. Well-
The above, as well as many other implemented
known examples are an open source system TeX [6] and
mathematical projects paved the way for the realization
commercial systems Wolfram Mathematica and
of a new idea – the creation of the World Digital Math-
WolframAlpha [7, 8]. With the help of communities of
ematical Library (WDML).
mathematicians, tools for mathematical content man-
agement are also actively developed. Examples are The idea of creating a WDML arose in 2002. The in-
MathJax system by American Mathematical Society, itial aim of this project was digitizing the entire set of
information system Math-Net.Ru (http://www.mathnet. mathematical literature (both modern and historical),
ru), developed at the Steklov Mathematical Institute of link it to the present literature, and make it clickable
the Russian Academy of Sciences, and the collection of (see [1, 23–28]). As noted in [25], the success of this
publicly available preprints arXiv.org (https://arxiv. project and its further impact on mathematics, science
org/). Now one of the largest digital mathematical li- and education could be the most significant event after
braries is Mizar (http://www.mizar.org/). This is a col- the invention of scientific journals and to become a pro-
lection of papers prepared in the Mizar system of formal totype for a new model of scientific and technical coop-
language, containing definitions, theorems and proofs eration, a new paradigm for future science in the elec-
[9, 10]. Mizar is one of the pioneering systems for tronic world. At the same time, the implementation of
mathematics formalization, which still has an active such a large project will inevitably cause a series of
user community. The project has been in constant de- problems. These problems and ways to overcome them
velopment since 1973. were analyzed in [27]. In particular, one of the recom-
mendations was the proposal to develop and coordinate
At present, scientific research in the field of mathe-
some local projects of creating DML (see ([27, 28]).
matics is increasingly associated with the use of modern
information technologies (cloud, semantic technologies, Basic plans for the construction of WDML in 2014-
etc.). These technologies are used in research conducted 2015 were discussed by various mathematical commu-
by distributed scientific groups, the preparation and nities and fixed in a number of documents (see [5, 29]).
dissemination of mathematical knowledge in electronic In particular, it was noted that the next step in the de-
form, the formation of mathematical digital libraries and velopment of the WDML project would be building
intellectual processing of their contents. Particular atten- information networks, knowledge-based, which are con-
tion is paid to creating a single information space by tained in mathematical publications. Many of the re-
integrating existing and organizing new digital mathe- search groups of mathematicians throughout the world
matical libraries (DML). Description of existing digital took part in the discussion of these ideas, including our
mathematical libraries with the indication of the purpos- group, which represented Kazan University.
327
In February 2016, in the Fields Institute (Toronto, mathematical content based on elements (classes) and
Ontario) by the Wolfram Foundation, the Fields Insti- their interrelations is proposed. The selection of classes
tute and the International Mathematical Union working of mathematical objects and the formation on their basis
group for the creation WDML, a Seminar on the Seman- of ontologies of knowledge areas will allow creating
tic Representation of Mathematical Knowledge was new tools for processing information, in particular, ex-
organized (https://www.fields.utoronto.ca/Programs/ tracting and processing formulas, searching for similar
science/15-16/semantic/). Our report on this symposium results, and so on.
was devoted to modeling and software solutions in the In our works [31–33], methods of structural analysis
area of semantic representation of mathematical of mathematical documents and the selection of objects
knowledge [30]. These results correspond to the general from them are proposed. In [22, 34], the digital ecosys-
ideology of the WDML-project in terms of semantic tem OntoMath is described, consisting of ontologies,
representation and processing of mathematical text analytics tools and applications, designed to control
knowledge and are a strategic direction of our group's mathematical knowledge. Semantic annotation of math-
research. In particular, they are connected to the project ematical texts is based on the ontology constructed
for the construction of the digital mathematical library within the framework of the Mocassin project, and on-
Lobachevskii DML, which is described below. tology of professional mathematics OntoMathPRO [35].
An important application developed on the basis of
2 Object Approach to the Scientific Digital these ontologies is a special software platform for pre-
Content Management paring a mathematical set of related data for publication
in the LOD cloud. Another important tool is the seman-
Managing of digital mathematical documents is a
tic search service by mathematical formulas [34]. An-
unique and complex task. This is due both to the pro-
other application of the OntoMath ecosystem is a rec-
cessing of mathematical formulas and to the specific
structure of a mathematical document consisting of a ommendation system for collections of physical and
logically connected sequence of definitions, theorems, mathematical documents. In particular, for a given doc-
proofs and references. The key idea identified in the ument based on selected objects of mathematical
knowledge, this system allows you to create a list of
WDML project documents is the development of object
“similar” documents (see [36]). These tools are included
classes for adequate description and research of mathe-
in the services of the Lobachevskii DML.
matical content: a new paradigm for representing digital
Figure 1 The Lobachevskii DML main page
328
was to not only create an archive of specialized litera-
3 Content, Structure and Services of Loba- ture for mathematics researchers, but also to form an
chevskii DML open extensive mathematical library for a wide range of
users, possessing a wide range of information pro-
3.1 Content and structure of the digital library cessing tools, including search tools. Of course, the ba-
Mathematical literature that has been published in sis of the Lobachevskii DML were research journals, as
Kazan University for more than two centuries of its ex- well as selected conference materials and monographs.
istence is fairly varied. All these publications have been The main emphasis in the selection of documents was
fully preserved in Scientific Library of Kazan Universi- made on the relevance and scientific novelty of materi-
ty. The Great Russian scientist N. I. Lobachevskii als included in the library.
played a great role in the development of this library. In The informational basis of digital collections in the
1825, he was elected a librarian and managed the library Lobachevskii DML was printed mathematical books
until 1835, combining these duties with the duties of the prepared at the Kazan University. At first, these editions
rector. With him, the scientific foundations of the col- were translated into digital format: the result of scan-
lection of Library funds were laid, the compilation of ning was a set of pdf-files containing articles from sci-
single catalogs began, Library has become public, ac- entific journals, proceedings of conferences, and mono-
cessible to residents of the city, and a special building graphs.
was erected for it. Today our library is named after Scientific journals are not only the most important
N. I. Lobachevskii. With nearly 6 million publications, section of the generated DML, but also collections, the
it is one of the largest libraries in Russia. easiest to process in DML, because these articles have a
The main goal of creating the Lobachevskii DML uniform structure and a standard set of metadata.
Figure 2 The page of LJM with MathML search tools
terials of international conferences on mathematics and
Lobachevskii DML structure is as follows:
mechanics;
• the digital collection of articles from the Lobachev-
skii Journal of Mathematics for 1998–2007 with seman- • the digital collection of articles from the journal
tic navigation tools, including search by formulas (see “Russian Mathematics (Iz. VUZ)”;
[14]); all the documents of this collection have been • the digital collection of articles from the journal
translated into the MathML-format (Figure 2); “Uchenye Zapiski Kazanskogo Universiteta. Seriya
• the digital collection of LJM articles from 2007 to Fiziko-Matematicheskie Nauki (Proceedings of Kazan
the present, published by Pleades Publishing LTD and University. Physics and Mathematics Series).
distributed by Springer Science+Business Media LLC; The digital collections of Lobachevskii DML are
• the digital collection “Proceedings of the shown in Figure 3.
N. I. Lobachevskii Mathematical Center” including ma-
329
Figure 3 Mathematical collections (https://lobachevskii-dml.ru/collections/)
this case was the selection of a range of pages for each
3.2 Services of Lobachevskii DML article included in the publication. Based on the de-
When designing Lobachevskii DML, we used the re- scribed information, the general file of the processed
sults we obtained earlier on the management of mathe- edition in automatic mode was divided into files con-
matical knowledge, as well as the developed methods of taining information about a separate article. Then, in the
structural and semantic analysis of mathematical docu- XML-file that characterizes the collection as a whole, a
ments [22, 31–36]. link to the file describing the article was added.
For the semantic presentation of documents included One of the new search services implemented in Lo-
in the digital library Lobachevskii DML, we developed bachevskii DML is OntoMath Formula Search Engine
an XML-language consisting of a set of tags; the rules (http://lobachevskii-dml.ru:8890/mathsearch/). It is a
for filling them in the form of DTD and XML Schema single-page web application that interacts through the
(see [14]). The XML-file describing each collection of SPARQL endpoint with a semantic view of publications
scientific documents was formed in several stages. Each using OpenLink Virtuoso (https://virtuoso.openlinksw.
of them assumed the development of a special software com/). This semantic representation is constructed using
tool that eliminates or simplifies the manual processing a semantic publication platform [34]. OntoMath Formu-
of a set of digitized documents [31–33, 37, 38]. This la Search finds mathematical formulas containing varia-
XML-file was supplemented with a bibliographic de- bles that denote a given mathematical concept. The
scription of the articles contained in the digitized edition search is performed in the collection of mathematical
(data on the journal number, the title of the conference documents presented in Lobachevskii DML (Figure 4).
proceedings, etc.) were added. The most difficult task in
Figure 4 OntoMathPRO Search User Interface
330
Currently, a new environment of scientific and edu- work of scientific projects Nos. 15-07-08522, 15-47-
cational activities is being actively formed, based on the 02472.
use of Internet technologies. In this regard, along with
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