Engineering and Automatic Construction of a Knowledge Graph “Mathematical Equations”
Main Article Content
Abstract
We propose an approach to engineering and implementing a knowledge graph for representing and storing knowledge about mathematical equations. We have developed a knowledge graph prototype that represents knowledge about the main types of mathematical equations, including algebraic equations, ordinary differential equations, partial differential equations, and integral equations. We designed the knowledge graph of mathematical equations as a mathematical artifact. We are integrating this artifact into the digital ecosystem of the Lobachevskii Digital Mathematical Library, therefore, we took into account the ecosystem's general compatibility requirements during the design. We have developed software tools for extracting and processing information about equations presented in digital libraries and electronic scientific resources. The current version of the knowledge graph prototype is based on the OntoMathPRO ontology of professional mathematics and a taxonomy of equations, built on information extracted from the web pages of the portal EqWorld "The World of Mathematical Equations." We expanded the OntoMathPRO ontology with new equation classes and new relationships to align with the equation type hierarchy presented on the EqWorld portal. We implemented a set of software modules that support the full cycle of knowledge graph generation, including a module for automatically extracting entities from external sources, a module for linking entities to OntoMathPRO ontology concepts, and a module for converting the acquired knowledge into an RDF representation and then storing it in a data warehouse. The knowledge graph supports SPARQL queries.
Article Details
References
2. EqWorld. The World of Mathematical Equations. URL: https://eqworld.ipmnet.ru/ (Accessed: 22.03.2026).
3. Lobachevskii Digital Mathematical Library. URL: https://lobachevskii-dml.ru/ (Accessed: 22.03.2026).
4. Numdam, the French digital mathematics library. URL: https://www.numdam.org/ (Accessed: 22.03.2026).
5. Encyclopedia of Mathematics. URL: https://encyclopediaofmath.org/ (Accessed: 22.03.2026).
6. Elizarov A.M., Lipachev E.K. Lobachevskii Digital Library in the Scientific Space of Mathematical Knowledge // Scientific and Technical Information Processing. 2023. Vol. 50, No. 1. P. 35–39. https://doi.org/10.3103/s0147688223010021
7. Elizarov A.M., Kirillovich A.V., Lipachev E.K., Nevzorova O.A. OntoMathPRO: an Ontology of Mathematical Knowledge // Doklady Mathematics. 2022. Vol. 106, No. 3. P. 429–435. https://doi.org/10.1134/S1064562422700016
8. Muromskiy A.A., Tuchkova N.P. Representation of Mathematical Concepts in the Ontology of Scientific Knowledge // Ontology of Designing. 2019. Vol. 9, No. 1 (31). P. 50–69. https://doi.org/10.18287/2223-9537-2019-9-1-50-69
9. Nevzorova O.A., Falileeva M.V., Kirillovich A.V.et al. OntoMathEdu Educational Ontology: Problems of Ontological Engineering // Pattern Recognition and Image Analysis. Advances in Mathematical Theory and Applications. 2023. Vol. 33, No. 3. P. 460–466. https://doi.org/10.1134/S1054661823030367
10. Ataeva O.M., Serebryakov V.A., Tuchkova N.P. Ontological Approach: Knowledge Representation and Knowledge Extraction // Lobachevskii J. Math. 2020. Vol. 41 (10). P. 1938–1948. https://doi.org/10.1134/S1995080220100030
11. Singhal A. Introducing the Knowledge Graph: things, not strings // Google Official Blog, 2012. URL: https://blog.google/products/search/introducing-knowledge-graph-things-not/ (Accessed: 22.03.2026)
12. Paulheim H. Knowledge graph refinement: A survey of approaches and evaluation methods // Semantic Web. 2017. Vol. 8. P. 489–508. https://doi.org/10.3233/SW-160218
13. Hogan A., Gutierrez C., Cochez M. et al. Data Graphs // In: Knowledge Graphs. Synthesis Lectures on Data, Semantics, and Knowledge. Springer, Cham, 2022. P. 5–23. https://doi.org/10.1007/978-3-031-01918-0_2
14. Ataeva O.M., Serebryakov V.A., Tuchkova N.P. Ontological Approach to a Knowledge Graph Construction in a Semantic Library // Lobachevskii J. Math. 2023. Vol. 44, No. 6. P. 2229–2239. https://doi.org/10.1134/S1995080223060471
15. Ataeva O.M., Serebryakov V.A., Tuchkova N.P. From Texts to Knowledge Graph in the Semantic Library LibMeta // Lobachevskii J. Math. 2024. Vol. 45, No. 5. P. 2211–2219. https://doi.org/10.1134/S1995080224602625
16. Khalov A.P., Ataeva O.M. Automatic and Semi-automatic Methods for Domain Knowledge-Graph Construction and Ontology Expansion // Russian Digital Libraries Journal. 2025. Vol. 28, No. 6. P. 1481–1519. https://doi.org /10.26907/1562-5419-2025-28-6-1481-1519
17. Ataeva O.M., Tuchkova N.P. Navigation with Large Language Models in Subject Domain of Ordinary Differential Equation // Lobachevskii J. Math. 2025. Vol. 46, No. 6. P. 2723–2735. https://doi.org/10.1134/S1995080225608227
18. Lipachev E.K., Muradymov B.R. Towards Building the Knowledge Graph of Mathematical Equations // Highly Available Systems. 2026. Vol. 22, No. 1. P. 41−46. https://doi.org/10.18127/j20729472-202601-08
19. Zajcev V.F., Polyanin A.D. Spravochnik po obyknovennym differenci-al'nym uravneniyam. M.: Fizmatlit, 2001. 576 s.
20. Zajcev V.F., Polyanin A.D. Spravochnik po differencial'nym uravneni-yam s chastnymi proizvodnymi pervogo poryadka. M.: Fizmatlit, 2003. 416 s.
21. Polyanin A.D. Spravochnik po linejnym uravneniyam matematicheskoj fiziki. M.: Fizmatlit, 2001. 575 s.
22. Polyanin A.D., Zajcev V.F. Nelinejnye uravneniya matematicheskoj fiziki. M.: Yurajt, 2017. 432 s.
23. Polyanin A.D., Manzhirov A.V. Spravochnik po integral'nym uravneniyam. M.: Fizmatlit, 2003. 369 s.
24. Polyanin A.D., Zaitsev V.F. Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems. CRC Press/Chapman and Hall, 2017. 1496 p. https://doi.org/10.1201/9781315117638
25. Polyanin A.D., Zaitsev V.F. Handbook of Exact Solutions for Ordinary Differential Equations, 2nd Edition (Updated and Extended). CRC Press, Boca Raton–New York, 2003. 816 p.
26. Polyanin A.D., Zaitsev V.F., Moussiaux A. Handbook of First Order Partial Differential Equations. CRC Press, 2001. 520 p. https://doi.org/10.1201/b16828
27. Polyanin A.D., Zaitsev V.F. Handbook of Nonlinear Partial Differential Equations, Second edition. CRC Press, 2012. 1912 p. https://doi.org/10.1201/b11412
28. Polyanin A.D., Manzhirov A.V. Handbook of Integral Equations, 2nd Edition. Chapman & Hall/CRC Press, Boca Raton–London, 2008. 1144 p.
https://doi.org/10.1201/9781420010558
29. Vinogradov I.M. (Red.) Matematicheskaya ehnciklopediya (v 5 tomah) M.: Sovetskaya ehnciklopediya (1977–1985).
30. Hazewinkel M. (Ed.) Encyclopaedia of Mathematics. An updated and annotated translation of the Soviet ‘Mathematical Encyclopaedia’. Vol. 1–10. Springer Dordrecht, 1988. https://doi.org/10.1007/978-94-009-6000-8
31. Ji S., Pan S., Cambria E., Marttinen P., Yu P.S. A Survey on Knowledge Graphs: Representation, Acquisition, and Applications // IEEE Transactions on Neural Networks and Learning Systems. 2022. Vol. 33, No. 2. P. 494–514.
https://doi.org/10.1109/TNNLS.2021.3070843
32. Kirillovich A.V., Nevzorova O.A., Lipachev E.K. OntoMathPRO 2.0 Ontology: Up-dates of Formal Model // Lobachevskii J. of Math. 2022. Vol. 43, No. 12. P. 3504–3514. https://doi.org/10.1134/S1995080222150136
33. Elizarov A.M., Kirillovich A.V., Lipachev E.K., Nevzorova O.A. New components of the OntoMathPRO ontology for representing math knowledge // Nauchnyj servis v seti Internet. 2023. № 25. S. 141–151. https://doi.org/10.20948/abrau-2023-32
34. RDF Mapping Language (RML). Unofficial Draft, 20 June 2024. URL: https://rml.io/specs/rml/ (Accessed: 22.03.2026)
35. Elizarov A.M., Kirillovich A.V., Lipachev E.K., Nevzorova O.A. Digital Ecosystem OntoMath as an Approach to Building the Space of Mathematical Knowledge // Russian Digital Libraries Journal. 2023. Vol. 26, No. 2. P. 154–202. https://doi.org/10.26907/1562-5419-2023-26-2-154-202
36. Elizarov A.M., Lipachev E.K. Lobachevskii Digital Library in the Scientific Space of Mathematical Knowledge // Scientific and Technical Information Processing. 2023. Vol. 50, No. 1. P. 35–39. https://doi.org/10.3103/s0147688223010021
37. Elizarov A., Lipachev E. Big math methods in Lobachevskii-DML // CEUR Workshop Proc. 2019. Vol. 2523. P. 59–72. https://ceur-ws.org/Vol-2523/invited08.pdf (Accessed: 22.03.2026).
This work is licensed under a Creative Commons Attribution 4.0 International License.
Presenting an article for publication in the Russian Digital Libraries Journal (RDLJ), the authors automatically give consent to grant a limited license to use the materials of the Kazan (Volga) Federal University (KFU) (of course, only if the article is accepted for publication). This means that KFU has the right to publish an article in the next issue of the journal (on the website or in printed form), as well as to reprint this article in the archives of RDLJ CDs or to include in a particular information system or database, produced by KFU.
All copyrighted materials are placed in RDLJ with the consent of the authors. In the event that any of the authors have objected to its publication of materials on this site, the material can be removed, subject to notification to the Editor in writing.
Documents published in RDLJ are protected by copyright and all rights are reserved by the authors. Authors independently monitor compliance with their rights to reproduce or translate their papers published in the journal. If the material is published in RDLJ, reprinted with permission by another publisher or translated into another language, a reference to the original publication.
By submitting an article for publication in RDLJ, authors should take into account that the publication on the Internet, on the one hand, provide unique opportunities for access to their content, but on the other hand, are a new form of information exchange in the global information society where authors and publishers is not always provided with protection against unauthorized copying or other use of materials protected by copyright.
RDLJ is copyrighted. When using materials from the log must indicate the URL: index.phtml page = elbib / rus / journal?. Any change, addition or editing of the author's text are not allowed. Copying individual fragments of articles from the journal is allowed for distribute, remix, adapt, and build upon article, even commercially, as long as they credit that article for the original creation.
Request for the right to reproduce or use any of the materials published in RDLJ should be addressed to the Editor-in-Chief A.M. Elizarov at the following address: amelizarov@gmail.com.
The publishers of RDLJ is not responsible for the view, set out in the published opinion articles.
We suggest the authors of articles downloaded from this page, sign it and send it to the journal publisher's address by e-mail scan copyright agreements on the transfer of non-exclusive rights to use the work.