Theory of Polysort Graphs of Knowledge-Learning

Abstract

The rapid pace of development of the digital economy poses new challenges for education systems, making it extremely urgent to accelerate the deployment of new technologies and processes that ensure the timely development of digital skills demanded by the economy. This, in turn, necessitates the search for new effective educational technologies and solutions.
The article discusses the theoretical foundations of the apparatus of special type graphs, consisting of vertices and directed edges of several sorts and called multi-sorted. Such apparatus is intended to create on its basis a toolkit for a system for the development of digital skills contributing to an increase in the efficiency of the development and implementation of educational processes. The advantage of the proposed toolkit is the ability to use it for the development, description, and configuration of educational content, as well as for managing the implementation of personalized educational processes. The article describes the algebra of polysort graphs, the basic operations on such graphs, examples of using this apparatus are given.

Author Biographies

Marina Sergeevna Polyanskaya, Lomonosov Moscow State University

Master's student, Software Engineer of the Open Information Technologies Lab, Faculty of Computational Mathematics and Cybernetics

Vladimir Alexandrovich Sukhomlin, Lomonosov Moscow State University

Head of the Open Information Technologies Lab, Faculty of Computational Mathematics and Cybernetics, Dr.Sci. (Technology), Professor, President of the Fund “League Internet-Media”

References

[1] Sukhomlin V.A., Zubareva E.V., Yakushin A.V. Methodological Aspects of the Digital Skills Concept. Sovremennye informacionnye tehnologii i IT-obrazovanie = Modern Information Technologies and IT-Education. 2017; 13(2):146-152. (In Russ., abstract in Eng.) DOI: https://doi.org/10.25559/SITITO.2017.2.253
[2] Sukhomlin V.A., Zubareva E.V., Namiot D.E., Yakushin A.V. Sistema razvitija cifrovyh navykov VMK MGU & Bazal't SPO. Metodika klassifikacii i opisanija trebovanij k sotrudnikam i soderzhaniju obrazovatel'nyh programm v sfere informacionnyh tehnologij [Digital Skills Development System]. MAKS Press: Basealt Publ., Moscow; 2020. (In Russ.)
[3] Popov E.V., Fridman G.F. Algorithmicheskie osnovy intellektualnikh robotov i iskusstvennogo intellekta [Algorithmic Basics of Intelligent Robots and Artificial Intelligence]. Nauka Publ., Moscow; 1976. (In Russ.)
[4] Pospelov D.A. Logiko-lingvisticheskie modeli v sistemakh upravleniya [Logical-linguistic models in control systems]. Energoizdat Publ., Moscow; 1981. (In Russ.)
[5] Ceruzzi P.E. A History of Modern Computing. Second Edition. MIT Press, Cambridge, MA, USA; 2003. (In Eng.)
[6] Gurin V.S., Kostrov E.V., Gavrilenko Yu.Yu., Saada D.F., Ilyushin E.A., Chizhov I.V. Knowledge Graph Essentials and Key Technologies. Sovremennye informacionnye tehnologii i IT-obrazovanie = Modern Information Technologies and IT-Education. 2019; 15(4);932-944. (In Eng.) DOI: https://doi.org/10.25559/SITITO.15.201904.932-944
[7] Harmelen F., Lifschitz V., Porter B. Handbook of Knowledge Representation. 1st Edition, vol. 1. Elsevier Science; 2007. (In Eng.)
[8] Piletski I.I., Batura M.P., Volarava N.A. System for Complex Analysis of Data from Internet Sources. In: Bogush V.A. (ed.) Proceedings of the 7th International Conference on BIG DATA and Advanced Analytics. Bestprint, Minsk; 2021. p. 198-209. Available at: https://libeldoc.bsuir.by/handle/123456789/43904 (accessed 14.09.2020). (In Russ., abstract in Eng.)
[9] Harary F. Graph Theory. Addison-Wesley Publishing Company, Boston; 1969. (In Eng.)
[10] Sukhomlin V.A. Algoritmicheskaja sistema dlja opisanija processov transljacii [Algorithmic System for Describing Translation Processes]. Programmirovanie = Programming and Computer Software. 1975; (2):77-83. (In Russ.)
[11] Lightfoot J.M. A Graph-Theoretic Approach to Improved Curriculum Structure and Assessment Placement. Communications of the IIMA. 2010; 10(2):5. Available at: http://scholarworks.lib.csusb.edu/ciima/vol10/iss2/5 (accessed 14.09.2020). (In Eng.)
[12] Joint Task Force on Cybersecurity Education. Cybersecurity Curricula 2017: Curriculum Guidelines for Post-Secondary Degree Programs in Cybersecurity. Association for Computing Machinery, New York, NY, USA; 2018. (In Eng.) DOI: https://doi.org/10.1145/3184594
[13] Li Z., Liu H., Zhang Z., Liu T. Shu J. Recalibration convolutional networks for learning interaction knowledge graph embedding. Neurocomputing. 2021; 427:118-130. (In Eng.) DOI: https://doi.org/10.1016/j.neucom.2020.07.137
[14] Wang H., Zhang F., Wang J., Zhao M., Li W., Xie X., Guo M. Exploring High-Order User Preference on the Knowledge Graph for Recommender Systems. ACM Transactions on Information Systems. 2019; 37(3):32. (In Eng.) DOI: https://doi.org/10.1145/3312738
[15] Wang Q., Mao Z., Wang B., Guo L. Knowledge Graph Embedding: A Survey of Approaches and Applications. IEEE Transactions on Knowledge and Data Engineering. 2017; 29(12):2724-2743. (In Eng.) DOI: https://doi.org/10.1109/TKDE.2017.2754499
[16] Zhao Y., Zhang A., Feng H., Li Q., Gallinari P., Ren F. Knowledge graph entity typing via learning connecting embeddings. Knowledge-Based Systems. 2018; 196:105808. (In Eng.) DOI: https://doi.org/10.1016/j.knosys.2020.105808
[17] Le N.-T., Vo B., Nguyen L.B.Q., Fujita H., Le B. Mining weighted subgraphs in a single large graph. Information Sciences. 2020; 514:149-165. (In Eng.) DOI: https://doi.org/10.1016/j.ins.2019.12.010
[18] Suchanek F.M., Kasneci G., Weikum G. Yago: a core of semantic knowledge. In: Proceedings of the 16th international conference on World Wide Web (WWW '07). Association for Computing Machinery, New York, NY, USA; 2007. p. 697-706. (In Eng.) DOI: https://doi.org/10.1145/1242572.1242667
[19] Steinmetz N., Sack H. Semantic Multimedia Information Retrieval Based on Contextual Descriptions. In: Cimiano P., Corcho O., Presutti V., Hollink L., Rudolph S. (ed.) The Semantic Web: Semantics and Big Data. ESWC 2013. Lecture Notes in Computer Science. 2013; 7882:382-396. Springer, Berlin, Heidelberg. (In Eng.) DOI: https://doi.org/10.1007/978-3-642-38288-8_26
[20] Zhang M., Geng G., Zeng S., Jia H. Knowledge Graph Completion for the Chinese Text of Cultural Relics Based on Bidirectional Encoder Representations from Transformers with Entity-Type Information. Entropy. 2020; 22(10):1168. (In Eng.) DOI: https://doi.org/10.3390/e22101168
[21] Bhatt Ah., Zhao J., Sheth A., Shalin V. Grafy znanij kak sredstvo uluchshenija iskusstvennogo intellekta [Knowledge graphs as a means of improving artificial intelligence]. Open Systems.DBMS. 2020; (03):24-26. Available at: https://elibrary.ru/item.asp?id=43925226 (accessed 14.09.2020). (In Russ.)
[22] Pommellet T., Lécué F. Feeding Machine Learning with Knowledge Graphs for Explainable Object Detection? CEUR Workshop Proceedings. 2019; 2456:277-280. Available at: http://ceur-ws.org/Vol-2456/paper72.pdf (accessed 14.09.2020). (In Eng.)
[23] Berrendorf M., Faerman E., Melnychuk V., Tresp V., Seidl T. Knowledge Graph Entity Alignment with Graph Convolutional Networks: Lessons Learned. In: Jose J. et al. (ed.) Advances in Information Retrieval. ECIR 2020. Lecture Notes in Computer Science. 2020; 12036:3-11. Springer, Cham. (In Eng.) DOI: https://doi.org/10.1007/978-3-030-45442-5_1
[24] St-Hilaire F. et al. A Comparative Study of Learning Outcomes for Online Learning Platforms. In: Roll I., McNamara D., Sosnovsky S., Luckin R., Dimitrova V. (ed.) Artificial Intelligence in Education. AIED 2021. Lecture Notes in Computer Science. 2021; 12749:331-337. Springer, Cham. (In Eng.) DOI: https://doi.org/10.1007/978-3-030-78270-2_59
[25] Giabbanelli P.J., Tawfik A.A., Gupta V.K. Learning Analytics to Support Teachers’ Assessment of Problem Solving: A Novel Application for Machine Learning and Graph Algorithms. In: Ifenthaler D., Mah D.K., Yau J.K. (ed.) Utilizing Learning Analytics to Support Study Success. Springer, Cham; 2019. p. 175-199. (In Eng.) DOI: https://doi.org/10.1007/978-3-319-64792-0_11
Published
2020-12-25
How to Cite
POLYANSKAYA, Marina Sergeevna; SUKHOMLIN, Vladimir Alexandrovich. Theory of Polysort Graphs of Knowledge-Learning. Modern Information Technologies and IT-Education, [S.l.], v. 16, n. 4, p. 940-950, dec. 2020. ISSN 2411-1473. Available at: <http://sitito.cs.msu.ru/index.php/SITITO/article/view/717>. Date accessed: 12 sep. 2025. doi: https://doi.org/10.25559/SITITO.16.202004.940-950.
Section
IT education: methodology, methodological support

Most read articles by the same author(s)

1 2 > >>