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Digital Ecosystem OntoMath: Mathematical Knowledge Analytics and Management

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Data Analytics and Management in Data Intensive Domains (DAMDID/RCDL 2016)

Abstract

A mathematical knowledge management technology is discussed, its basic ideas, approaches and results are based on targeted ontologies in the field of mathematics. The solution forms the basis of the specialized digital ecosystem OntoMath which consists of a set of ontologies, text analytics tools and applications for managing mathematical knowledge. The studies are in line with the project aimed to create a World Digital Mathematical Library whose objective is to design a distributed system of interconnected repositories of digitized versions of mathematical documents.

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References

  1. Knuth, D.E.: The TeX Book. Addison-Wesley Publishing Company, Reading (1986)

    MATH  Google Scholar 

  2. Wolfram, S.: A New Kind of Science. Wolfram Media Inc., Champaign (2002)

    MATH  Google Scholar 

  3. Wolfram, S.: An Elementary Introduction to the Wolfram Language. Wolfram Media Inc., Champaign (2015)

    Google Scholar 

  4. Chebukov, D.E., Izaak, A.D., Misyurina, O.G., Pupyrev, Y.A., Zhizhchenko, A.B.: Math-Net.Ru as a digital archive of the russian mathematical knowledge from the XIX century to today. In: Carette, J., Aspinall, D., Lange, C., Sojka, P., Windsteiger, W. (eds.) CICM 2013. LNCS (LNAI), vol. 7961, pp. 344–348. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39320-4_26

    Chapter  Google Scholar 

  5. Carette, J., Farmer, William M.: A review of mathematical knowledge management. In: Carette, J., Dixon, L., Coen, C.S., Watt, Stephen M. (eds.) CICM 2009. LNCS (LNAI), vol. 5625, pp. 233–246. Springer, Heidelberg (2009). doi:10.1007/978-3-642-02614-0_21

    Chapter  Google Scholar 

  6. Lange, C.: Ontologies and languages for representing mathematical knowledge on the semantic web. Semant. Web 4(2), 119–158 (2013). doi:10.3233/SW-2012-0059

    Google Scholar 

  7. Ion, P.D.F.: Mathematics and the world wide web. In: Carette, J., Aspinall, D., Lange, C., Sojka, P., Windsteiger, W. (eds.) CICM 2013. LNCS (LNAI), vol. 7961, pp. 230–245. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39320-4_15

    Chapter  Google Scholar 

  8. Kohlhase, M.: Mathematical knowledge management: transcending the one-brain-barrier with theory graphs. Newslett. Eur. Math. Soc. 92, 22–27 (2014)

    MathSciNet  MATH  Google Scholar 

  9. Elizarov, A., Kirillovich, A., Lipachev, E., Nevzorova, O., Solovyev, V., Zhiltsov, N.: Mathematical knowledge representation: semantic models and formalisms. Lobachevskii J. Math. 35(4), 347–353 (2014). doi:10.1134/S1995080214040143

    Article  MathSciNet  MATH  Google Scholar 

  10. Naumowicz, A., Korniłowicz, A.: A brief overview of Mizar. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 67–72. Springer, Heidelberg (2009). doi:10.1007/978-3-642-03359-9_5

    Chapter  Google Scholar 

  11. Bancerek, G., Byliński, C., Grabowski, A., Korniłowicz, A., Matuszewski, R., Naumowicz, A., Pa̧k, K., Urban, J.: Mizar: state-of-the-art and beyond. In: Kerber, M., Carette, J., Kaliszyk, C., Rabe, F., Sorge, V. (eds.) CICM 2015. LNCS (LNAI), vol. 9150, pp. 261–279. Springer, Cham (2015). doi:10.1007/978-3-319-20615-8_17

    Chapter  Google Scholar 

  12. Elizarov, A.M., Lipachev, E.K., Malakhaltsev, M.A.: Web technologies for mathematicians: the basics of MathML. In: A Practical Guide. Fizmatlit, Moscow (2010). (in Russian)

    Google Scholar 

  13. Kohlhase, M.: An Open Markup Format for Mathematical Documents (Version 1.2). LNAI, vol. 4180. Springer, Heidelberg (2006). http://omdoc.org/pubs/omdoc1.2.pdf

  14. Iancu, M., Kohlhase, M., Rabe, F., Urban, J.: The mizar mathematical library in OMDoc: translation and applications. J. Autom. Reason. 50(2), 191–202 (2013). Springer

    Article  MathSciNet  MATH  Google Scholar 

  15. Kohlhase, M.: Semantic Markup in TeX/LaTeX. http://ctan.altspu.ru/macros/latex/contrib/stex/sty/stex/stex.pdf

  16. Dehaye, P.-O., et al.: Interoperability in the OpenDreamKit project: the math-in-the-middle approach. In: Kohlhase, M., Johansson, M., Miller, B., de Moura, L., Tompa, F. (eds.) CICM 2016. LNCS (LNAI), vol. 9791, pp. 117–131. Springer, Cham (2016). doi:10.1007/978-3-319-42547-4_9

    Chapter  Google Scholar 

  17. Elizarov, A.M., Kirilovich, A.V., Lipachev, E.K., Nevzorova, O.A.: Mathematical knowledge management: ontological models and digital technology. In: CEUR Workshop Proceedings, vol. 1752, pp. 44–50 (2016). http://ceur-ws.org/Vol-1752/paper08.pdf

  18. Staab, S., Studer, R. (eds.): Handbook on Ontologies. Springer, Heidelberg (2003). (Republished in 2009)

    Google Scholar 

  19. Briscoe, G., De Wilde, P.: Digital ecosystems: evolving service-oriented architectures. In: Conference on Bio Inspired Models of Network, Information and Computing Systems. IEEE Press (2006). arXiv:0712.4102v6. https://arxiv.org/pdf/0712.4102v6.pdf

  20. Digital Ecosystem Convergence between IT, Telecoms, Media and Entertainment: Scenarios to 2015. http://www3.weforum.org/docs/WEF_DigitalEcosystem_Scenario2015_ExecutiveSummary_2010.pdf

  21. Amritesh, C.J.: Digital ecosystem for knowledge, learning and exchange: exploring socio-technical concepts and adoption. In: Basile Colugnati, F.A., et al. (eds.) OPAALS 2010. LNICST, vol. 67, pp. 44–61. Springer, Heidelberg (2010)

    Google Scholar 

  22. David, C., Ginev, D., Kohlhase, M., Corn, J.: eMath 3.0: building blocks for a social and semantic Web for online mathematics & elearning. In: Mierluş-Mazilu I. (ed.) Proceedings of the 1st International Workshop on Mathematics and ICT: Education, Research and Applications, pp. 13–23. Conspress, Bucureşti (2010). http://kwarc.info/kohlhase/papers/malog10.pdf

  23. David, C., Ginev, D., Kohlhase, M., Matican, B., Mirea, S.: A framework for semantic publishing of modular content objects. In: CEUR Workshop Proceedings, vol. 721, pp. 1–12 (2011). http://ceur-ws.org/Vol-721/paper-03.pdf

  24. Kohlhase, M., Corneli, J., David, C., Ginev, D., Jucovschi, C., Kohlhase, A., Lange, C., Matican, B., Mirea, S., Zholudev, V.: The planetary system: web 3.0 & active documents for STEM. In: Sato, M., Matsuoka, S., Sloot, P.M., Dick Albada, G., Dongarra, J. (eds.) Procedia Computer Science (4) (Special issue: Proceedings of the International Conference on Computational Science), pp. 598–607. Elsevier (2011)

    Google Scholar 

  25. Bouche, T.: Digital mathematics libraries: the good, the bad, the ugly. Math. Comput. Sci. 3(3), 227–241 (2010). doi:10.1007/s11786-010-0029-2

    Article  MATH  Google Scholar 

  26. Sylwestrzak, W., Borbinha, J., Bouche, T., Nowinski, A., Sojka P.: EuDML – towards the European digital mathematics library. In: Sojka P. (ed.) Towards a Digital Mathematics Library. Paris, 7–8 July 2010, pp. 11–26. Masaryk University Press, Brno (2010). http://dml.cz/bitstream/handle/10338.dmlcz/702569/DML_003-2010-1_5.pdf

  27. Bouche, T.: Towards a World Digital Library: Mathdoc, Numdam and EuDML Experiences. UMI, La Sapienza, Roma (2016). http://www.mat.uniroma1.it/sites/default/import-files/biblioteca/SEMINARIO2016/bouche.pdf

  28. Elizarov, A., Lipachev, E., Zuev, D.: Mathematical content semantic markup methods and open scientific e-journals management systems. In: Klinov, P., Mouromtsev, D. (eds.) KESW 2014. CCIS, vol. 468, pp. 242–251. Springer, Cham (2014). doi:10.1007/978-3-319-11716-4_22

    Google Scholar 

  29. Elizarov, A.M., Zuev, D.S., Lipachev E.K.: Open scientific e-journals management systems and digital libraries technology. In: CEUR Workshop Proceedings, vol. 1108, pp. 102–111 (2013). http://ceur-ws.org/Vol-1108/paper13.pdf

  30. Elizarov, A.M., Zuev, D.S., Lipachev, E.K.: Infrastructure of electronic scientific journal and cloud services supporting lifecycle of electronic publications. In: CEUR Workshop Proceedings, vol. 1297, pp. 156–159 (2014). http://ceur-ws.org/Vol-1297/156-159_paper-23.pdf

  31. Elizarov, A.M., Zuev, D.S., Lipachev, E.K.: Electronic scientific journal management systems. Sci. Tech. Inf. Process. 41(1), 66–72 (2014). doi:10.3103/S0147688214010109

    Article  Google Scholar 

  32. Elizarov, A.M., Zuev, D.S., Lipachev, E.K., Malakhaltsev, M.A.: Services structuring mathematical content and integration of digital mathematical collections at scientific information space. In: CEUR Workshop Proceedings, vol. 934, pp. 309–312 (2012). http://ceur-ws.org/Vol-934/paper47.pdf

  33. Elizarov, A.M., Lipachev, E.K., Haidarov, S.M.: Automated processing service system of large collections of scientific documents. In: CEUR Workshop Proceedings, vol. 1752, pp. 58–64 (2016). http://ceur-ws.org/Vol-1752/paper10.pdf

  34. Jackson, A.: The digital mathematics library. Not. AMS 50(4), 918–923 (2003). http://www.ams.org/notices/200308/comm-jackson.pdf

  35. The Digital Mathematical Library Project. Status, August 2005. http://www.math.uiucedu/~tondeur/DML04.pdf

  36. Digital Mathematics Library: a Vision for the Future. International Mathematical Union (2006). http://www.mathunion.org/fileadmin/IMU/Report/dml_vision.pdf

  37. Tondeur, P.: WDML: the world digital mathematics library. The evolution of mathematical communication in the age of digital libraries. In: IMA Workshop, December 8–9 (2006). http://www.math.uiuc.edu/~tondeur/WDML_IMA_DEC2006.pdf

  38. Pitman, J., Lynch, C.: Planning a 21st century global library for mathematics research. Not. AMS 61(7), 776–777 (2014). http://www.ams.org/notices/201407/rnoti-p776.pdf

  39. Developing a 21st century global library for mathematics research. Washington, D.C.: The National Academies Press, Washington, D.C (2014). arxiv.org/pdf/1404.1905, http://www.nap.edu/catalog/18619/developing-a-21st-century-global-library-for-mathematics-research

  40. Olver, P.J.: The world digital mathematics library: report of a panel discussion. In: Proceedings of the International Congress of Mathematicians, 13–21 August 2014, Seoul, Korea, Kyung Moon SA, vol. 1, pp. 773–785 (2014)

    Google Scholar 

  41. Elizarov, A.M., Zhiltsov, N.G., Kirillovich, A.V., Lipachev, E.K., Nevzorova, O.A., Solovyev, V.D.: The OntoMath ecosystem: ontologies and applications for math knowledge management. In: Semantic Representation of Mathematical Knowledge Workshop, 5 February 2016. http://www.fields.utoronto.ca/video-archive/2016/02/2053–14698

  42. Todeschini, R., Baccini, A.: Handbook of Bibliometric Indicators: Quantitative Tools for Studying and Evaluating Research. Wiley-VCH Verlag (2016)

    Google Scholar 

  43. Nevzorova, O.A., Birialtsev, E.V., Zhiltsov, N.G.: Mathematical text collections: annotation and application for search tasks. Sci. Tech. Inf. Process. 40(6), 386–395 (2013)

    Article  Google Scholar 

  44. Nevzorova, O., Zhiltsov, N., Zaikin, D., Zhibrik, O., Kirillovich, A., Nevzorov, V., Birialtsev, E.: Bringing math to LOD: a semantic publishing platform prototype for scientific collections in mathematics. In: Alani, H., et al. (eds.) ISWC 2013. LNCS, vol. 8218, pp. 379–394. Springer, Heidelberg (2013). doi:10.1007/978-3-642-41335-3_24

    Chapter  Google Scholar 

  45. Kamareddine, F., Wells, J.B.: Computerizing mathematical text with mathlang. Electron. Notes Theor. Comput. Sci. 205, 5–30 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  46. Solovyev, V., Zhiltsov, N.: Logical structure analysis of scientific publications in mathematics. In: Akerkar, R. (ed.) Proceedings of the International Conference on Web Intelligence, Mining and Semantics (WIMS 2011), vol. 21, pp. 1–9. ACM DL (2011). doi:10.1145/1988688.1988713

  47. OWL 2 Web Ontology Language. RDF-Based Semantics (Second Edition). W3C Recommendation 11 December 2012. https://www.w3.org/2012/pdf/REC-owl2-rdf-based-semantics-20121211.pdf

  48. Nevzorova, O., Zhiltsov, N., Kirillovich, A., Lipachev, E.: OntoMathPRO ontology: a linked data hub for mathematics. In: Klinov, P., Mouromstev, D. (eds) KESW 2014. CCIS, vol. 468, pp. 105–119. Springer, Heidelberg (2014). doi:10.1007/978-3-319-11716-4_9

  49. Elizarov, A.M., Lipachev, E.K., Nevzorova, O.A., Solov’ev, V.D.: Methods and means for semantic structuring of electronic mathematical documents. Doklady Math. 90(1), 521–524 (2014). doi:10.1134/S1064562414050275

  50. Elizarov, A.M., Kirillovich, A.V., Lipachev, E.K., Zhizhchenko, A.B., Zhil’tsov, N.G.: Mathematical knowledge ontologies and recommender systems for collections of documents in physics and mathematics. Doklady Math. 93(2), 231–233 (2016). doi:10.1134/S1064562416020174

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgement

This work was funded by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities, grant agreement no. 1.2368.2017).

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Elizarov, A., Kirillovich, A., Lipachev, E., Nevzorova, O. (2017). Digital Ecosystem OntoMath: Mathematical Knowledge Analytics and Management. In: Kalinichenko, L., Kuznetsov, S., Manolopoulos, Y. (eds) Data Analytics and Management in Data Intensive Domains. DAMDID/RCDL 2016. Communications in Computer and Information Science, vol 706. Springer, Cham. https://doi.org/10.1007/978-3-319-57135-5_3

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  • DOI: https://doi.org/10.1007/978-3-319-57135-5_3

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