Formal Model of Multimodal Educational Knowledge Graph for Intelligent Tutoring Systems
Abstract
The paper presents a formal model of a Multimodal Educational Knowledge Graph (MEKG) designed for structured knowledge representation in intelligent tutoring systems. A mathematical model MEKG = ⟨E, R, A, M, T, F⟩ is proposed, integrating heterogeneous entities (concepts, skills, learning materials, assignments), typed relations (prerequisite, part-of, assessment), multimodal attributes, and temporal dynamics. Formal properties of the model are defined: acyclicity of prerequisite relations, competency coverage completeness, and consistency of multimodal representations. Graph integrity verification algorithms and versioning mechanisms are developed. A comparative analysis with existing approaches, including Russian knowledge engineering research, is conducted. Experimental evaluation on a programming course (215 concepts, 312 prerequisite relations) confirmed the model's applicability for automated knowledge diagnostics and learning personalization: integration with a knowledge tracing system improved prediction accuracy (AUC) by 2.5 percentage points.
References
L. Li and Z. Wang, “Knowledge Graph Enhanced Intelligent Tutoring System Based on Exercise Representativeness and Informativeness,” International Journal of Intelligent Systems, vol. 2023, no. 2578286, pp. 1–19, 2023; doi:10.1155/2023/2578286
B. Abu-Salih and S. Alotaibi, “A Systematic Literature Review of Knowledge Graph Construction and Application in Education,” Heliyon, vol. 10, no. 3, p. e25383, 2024; doi:10.1016/j.heliyon.2024.e25383
D. El Alaoui, J. Riffi, A. Sabri et al., “Deep Learning Based Knowledge Tracing in Intelligent Tutoring Systems,” Scientific Reports, vol. 15, no. 07422, 2025.
A. Hogan, E. Blomqvist, M. Cochez et al., “Knowledge Graphs,” ACM Computing Surveys, vol. 54, no. 4, pp. 1–37, 2021; doi:10.1145/3447772
S. Ji, S. Pan, E. Cambria et al., “A Survey on Knowledge Graphs: Representation, Acquisition, and Applications,” IEEE Transactions on Neural Networks and Learning Systems, vol. 33, no. 2, pp. 494–514, 2022; doi:10.1109/TNNLS.2021.3070843
P. Chen, Y. Lu, V. W. Zheng et al., “A Review: Knowledge Reasoning over Knowledge Graph,” Expert Systems with Applications, vol. 141, p. 112948, 2020; doi:10.1016/j.eswa.2019.112948
J. Pu, X. Wang, C. Liu et al., “Graph Neural Network Based Intelligent Tutoring System: A Survey,” Neurocomputing, vol. 600, p. 128142, 2024.
Q. Huang and Y. Zeng, “Enhancing the Recommendation of Learning Resources for Learners via an Advanced Knowledge Graph,” Applied Sciences, vol. 15, no. 8, no. 4204, 2025.
Y. Yang, X. Shen, and E. Chen, “A Comprehensive Survey on Deep Learning Techniques in Educational Data Mining,” Data Science and Engineering, vol. 10, pp. 1–28, 2025.
“IEEE Standard for Learning Object Metadata,” IEEE Std 1484.12.1-2020, 2020; doi:10.1109/IEEESTD.2020.9262118
J. Yu, C. Wang, G. Luo et al., “MOOCCube: A Large-scale Data Repository for NLP Applications in MOOCs,” in Proc. of the 58th Annual Meeting of the Association for Computational Linguistics (ACL), 2020, pp. 3135–3142; doi:10.18653/v1/2020.acl-main.285
T. Baltrusaitis, C. Ahuja, and L. P. Morency, “Multimodal Machine Learning: A Survey and Taxonomy,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 41, no. 2, pp. 423–443, 2019; doi:10.1109/TPAMI.2018.2798607
P. Xu, X. Zhu, and D. A. Clifton, “Multimodal Learning with Transformers: A Survey,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 45, no. 10, pp. 12113–12132, 2023; doi:10.1109/TPAMI.2023.3275156
S. Shen, E. Chen, Q. Liu et al., “A Survey of Knowledge Tracing: Models, Variants, and Applications,” IEEE Transactions on Learning Technologies, vol. 17, pp. 1898–1912, 2024.
H. Su, X. Liu, S. Yang et al., “Deep Knowledge Tracing with Learning Curves,” Frontiers in Psychology, vol. 14, no. 1150329, 2023; doi:10.3389/fpsyg.2023.1150329
T. A. Gavrilova, D. V. Kudryavtsev, and D. I. Muromtsev, Knowledge Engineering: Models and Methods, Saint Petersburg, Russia: Lan, 2016 (in Russian).
G. V. Rybina, Fundamentals of Building Intelligent Systems: A Textbook, Moscow: Finance and Statistics; INFRA-M, 2010 (in Russian).
Y. A. Zagorulko and G. B. Zagorulko, “Ontologies and Their Practical Application in Knowledge-Based Systems,” in Proceedings of the All-Russian Conference with International Participation “Knowledge – Ontologies – Theories” (KONT-2015), Novosibirsk, Russia, 2015, vol. 1, pp. 137–146 (in Russian).
Z. Li, Z. Wang, W. Wang et al., “Retrieval-Augmented Generation for Educational Application: A Systematic Survey,” Computers and Education: Artificial Intelligence, vol. 8, no. 100417, 2025.
C. W. Okonkwo and A. Ade-Ibijola, “Retrieval-Augmented Generation (RAG) Chatbots for Education: A Survey of Applications,” Applied Sciences, vol. 15, no. 8, p. 4234, 2025.
T. H. Cormen, C. E. Leiserson, R. L. Rivest et al., Introduction to Algorithms, 4th ed. Cambridge, MA, USA: MIT Press, 2022.
J. Devlin, M. W. Chang, K. Lee et al., “BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding,” in Proceedings of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (NAACL-HLT), 2019, pp. 4171–4186; doi:10.18653/v1/N19-1423
A. Radford, J. W. Kim, C. Hallacy et al., “Learning Transferable Visual Models From Natural Language Supervision,” in Proceedings of the 38th International Conference on Machine Learning (ICML), 2021, pp. 8748–8763.
C. Piech, J. Bassen, J. Huang et al., “Deep Knowledge Tracing,” in Advances in Neural Information Processing Systems, vol. 28, 2015, pp. 505–513.
A. T. Corbett and J. R. Anderson, “Knowledge Tracing: Modeling the Acquisition of Procedural Knowledge,” User Modeling and User-Adapted Interaction, vol. 4, no. 4, pp. 253–278, 1994; doi:10.1007/BF01099821
M. Canal-Esteve and Y. Gutierrez, “Educational Material to Knowledge Graph Conversion: A Methodology to Enhance Digital Education,” in Proc. of the 1st Workshop on Knowledge-Augmented Language Models (KaLLM), Association for Computational Linguistics (ACL), 2024.
Y. Lu, D. Wang, P. Chen et al., “RadarMath: An Intelligent Tutoring System for Math Education,” in Proc. of the 35th AAAI Conference on Artificial Intelligence, vol. 35, 2021, pp. 16087–16090.
S. Zhang, Q. Xie, and G. Wang, “An Adaptive Learning Method Based on Knowledge Graph,” Frontiers in Educational Research, vol. 6, no. 6, pp. 1–12, 2023.
This work is licensed under a Creative Commons Attribution 4.0 International License.
