• Xenia Naidenova Military Medical Academy, Saint Petersburg, Russian Federation
  • Sergey Kurbatov Research Center of Electronic Computer Engineering, Moscow, Russian Federation
  • Vyacheslav Ganapolsky Military Medical Academy, Saint Petersburg, Russian Federation



planimetric tasks, natural language analysis, cognitive approach, dynamic visualization, intelligent system


A new cognitive approach is proposed for understanding the texts of planimetric tasks and for visualizing the task conditions to complement the syntactic-semantical sentence parsing. Two main difficulties in understanding texts of plane geometry tasks are observed: the ellipticity and vagueness of texts. To overcome the difficulties in understanding the task conditions it is proposed constructing cognitive models of objects and relations between them. The proposed cognitive approach is incorporated in an integrated system for automatic solving planimetric tasks with the natural language interface. The interactive visualization has been developed in the system. It depicts the syntactic and semantic structures as a result of natural language text analysis and searching for task solution. This visualization allows the users to obtain explanations associated with any elements of the images and to correct the tasks’ texts in dialog with the system. The destiny of the system is to serve for training schoolchildren in the domain of Euclidean geometry. The cognitive approach proposed can be a first step to automated analyzing plane geometry texts, in perspective, as a cognitively controlled parsing.


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Apresyan, J. D., Boguslavsky, I., Iomdin, L., & Sannikov, V. (2010). Theoretical problem of Russian syntax; interaction of grammar and vocabulary. Moscow, Russia: Languages of Slavonic Cultures.

Culicover, P. W., & Jackendoff, R. (2006). The simpler syntax hypothesis. Trends in cognitive sciences, 10(9), 413-418.

Evans, V., & Green, M. (2006). Cognitive linguistics: An introduction. Edinburgh, Scotland: Edinburgh University Press.

Jurafsky, D. (1993). A cognitive model of sentence interpretation: The construction grammar approach. International Computer Science Institute. Retrieved from

JSXGraph Reference. Retrieved from

Kenyon-Dean, K., Cheung, J. C. K., & Precup, D. (2016). Verb phrase ellipsis resolution using discriminative and margin-infused algorithms. In Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing (pp. 1734-1743). Retrieved from

Khakhalin, G. K., Kurbatov, S. S., Naidenova, X., & Lobzin, A. P. (2012). Integration of the Image and NL-text Analysis/Synthesis Systems. In Intelligent Data Analysis for Real-Life Applications: Theory and Practice (pp. 160-185). IGI Global.

Kurbatov, S., Naidenova, X., & Ganapol’skii, V. (2019). Resolving ellipses in planimetric tasks as cognitive process. In Masalova, S. I., & Solovyev, V. D. (Eds.). Proceedings of the VIIth International Scientific Conference on Cognitive Modeling in Science, Culture, Education (CMSCE-2019). Part 2. Cognitive Modeling in Linguistics (CML-2019) (pp. 114-121). Rostov-on-Don, Russia: Science and Studies Foundation.

Kurbatov, S., Fominykh, & Vorobyev, A. (2019). Interactive visualization of cognitive structure in an integral system. In Proceedings of the 17th National Conference on Artificial Intelligence with International Participation (CAI-2019). Vol. 2 (pp. 222-230). Ulyanovsk: USTU.

Kurbatov, S., & Vorobyev, A. (2016). Ontological solver of geometry problems in natural language description. In Proceedings of the 15th National Conference on Artificial Intelligence with International Participation (CAI-2016). Vol. 1 (pp. 56-63). Smolensk, Russia: Universum.

Langacker, R. W. (1990). Subjectification. Cognitive Linguistics (includes Cognitive Linguistic Bibliography), 1(1), 5-38.

Liu, Z., Gonzalez, E., & Gillick., D. (2016). Exploring the steps of VPE. In Proceedings of the Workshop on Conference Resolution Beyond OntoNotes (CORBON 2016), co-located with NAACL (pp. 32-40). San Diego, California: Association for Computational Linguistics.

Lobzin, A., Khakhalin, G., Kurbatov, S., & Litvinovich, A. (2016). Integration based on natural language and image ontology in the system Text-To-Picture. In Proceedings of the 8th Scientific-Practical Conference Integrated Models and Soft Computing in Artificial Intelligence. Vol. 1 (pp. 296-305). Moscow, Russia: Physical-Mathematical Literature.

MathJax Documentation, Release 3.0. (2020). Retrieved from

McShane, M., & Babkin, P. (2015). Automatic Ellipsis Resolution: Recovering Covert Information from Text. In Proceedings of the Twenty Ninth AAAI Conference on Artificial Intelligence. pp. 572- 578. Palo Alto, California: The AAAI Press. Retrieved from

McShane, M., & Babkin, P. (2016). Detection and resolution of verb phrase ellipsis. LiLT (Linguistic Issues in Language Technology), 13, 1-36. Retrieved from

Mel’čuk, I. A. (2018). Anna Wierzbicka, Semantic Decomposition, and the Meaning-Text Approach. Russian Journal of Linguistics, 22(3), 521-538.

Naidenova X. A., Kurbatov S. S., & Ganapol’skii, V. P. (2018). An analysis of plane task text ellipticity and the possibility of ellipses reconstructing based on cognitive modelling geometric objects and actions. In A. Elisarov, & N. Loukachevich (Eds.). In Proceedings of Computational Models in Language and Speech Workshop (CMLS 2018) co-located with the 15th TEL International Conference on Computational and Cognitive Linguistics (TEL-2018). Vol. 2 (pp. 70-85). Kazan, Russia: Academy of Sciences of RT. Retrieved from

Sechenov, I. M. (2008). Elements of thoughts. Saint-Petersburg, Russia: “Piter”.

Schuster, S., Nivre, J., & Manning, C. D. (2018). Sentences with gapping: Parsing and reconstructing elided predicates. In Proceedings of the 2018 Conference on the North America Chapter of the Association for Computational Linguistics: Human Language Technologies (NAACL 2018) (pp. 1156-1168. Retrieved from

Zhao, G. (2016). A cognitive approach to ellipsis. Theory and Practice in Language Studies, 6(2), 372-377.




How to Cite

Naidenova, X. ., Kurbatov, S. ., & Ganapolsky, V. . (2020). COGNITIVE MODELS IN PLANIMETRIC TASK TEXT PROCESSING. International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE), 8(1), 25–35.