Abstract
The paper is devoted to the problem of computer simulation of inductive and deductive reasonings based on the example of automatic solutions to planimetric problems. The study has been carried out using an experimental system that includes a natural language interface. The deductive component of the system is based on the geometry axiomatics; the inductive component is based on the Polya concept. We have described the interaction of components in solving problems and given some solution examples, while noting the important role of cognitive patterns for formalizing the problem description in a natural language, supporting the solver, and generating a drawing. We have emphasized the applied value of the research results for the education sector.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Fominykh, I.B.: Image engineering, creative tasks, emotional assessments. Des. Ontol. 8(2), 28 (2018)
Polya, G.: Mathematical Discovery: On Understanding, Learning and Teaching Problem, Solving, p. 432. Wiley, Hoboken (1981)
Devlin, K.: Modeling real reasoning, CSLI, Stanford University (2007)
Kulik, B.A.: Modeling reasoning by algebraic methods, educational resources and technologies 1(4) (2014)
Varshavskij, P.R., Eremeev, A.P.: Case-based reasoning modeling in intelligent decision support systems, Russia (2009)
Gan, W., Yu, X.: Automatic understanding and formalization of natural language geometry problems using syntax-semantics models. Int. J. Innov. Compute. Inf. Control ICIC 14(1), 83–98 (2018)
Cobbe, K., et al.: Training Verifiers to Solve Math Word Problems, 18 November 2021. arXiv:2110.14168v2 [clog] (2021)
Seo, M., Hajishirzi, H., Farhadi, A., Etzioni, O., Malcolm, C.: Solving geometry problems: combining text and diagram interpretation. http://geometry.allenai.org/assets/emnlp2015.pdf
Brown, T.B., et al.: Language Models are Few-Shot Learners, 22 July 2020. arXiv:2005.14165v4 [cs.CL] (2020)
Podkolzin, A.S.: The study of logical processes by computer simulation. J. Intell. Syst. Theory Appl. 20, 164–168 (2016)
Kurbatov, S.: Linguistic processor of the integrated system for solving planimetric problems. Comput Sci. Int. J. Knowl. Based Intell. Eng. Syst. (2021)
Kurbatov, S., Fominykh, I., Vorobyev, A.: Cognitive patterns for semantic presentation of natural-language descriptions of well-formalizable problems. In: Kovalev, S.M., Kuznetsov, S.O., Panov, A.I. (eds.) RCAI 2021. LNCS (LNAI), vol. 12948, pp. 317–330. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-86855-0_22
Naidenova, X., Kurbatov, S., Ganapolsky, V.: Cognitive models in planimetric task text processing. Int. J. Cogn. Res. Sci. Eng. Educ. 8(1), 25–35 (2020)
Wang, K., Su, Z.: Automated geometry theorem proving for human-readable proofs. In: Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, Buenos Aires, Argentina, 25–31 July 2015
Baeta, N., Quaresma, P.: Open geometry prover community project. In: Proceedings of the Thirteenth International Conference on Automated Deduction in Geometry (ADG 2021), Electronic Proceedings in Theoretical Computer Science (EPTCS), vol. 352, December 2021. https://doi.org/10.4204/EPTCS.352.14
Quaresma, P.: Automated deduction and knowledge management in geometry. Math. Comput. Sci. 14(4), 673–692 (2020). https://doi.org/10.1007/s11786-020-00489-7
Gan, W., Sun, Y., Sun, Y.: Knowledge structure enhanced graph representation learning model for attentive knowledge tracing. Int. J. Intell. Syst. 37, 2012–2045 (2022). https://doi.org/10.1002/int.22763
Gan, W., Yu, X., Wang, M.: Automatic understanding and formalization of plane geometry proving problems in natural language: a supervised approach. Int. J. Artif. Intell. Tools 28(4), 1940003 (2019). https://doi.org/10.1142/S0218213019400032
Lu, P., et al.: Theorem-aware geometry problem solving with symbolic reasoning and theorem prediction the 35th Conference on Neural Information Processing Systems (NeurIPS 2021) Workshop on Math AI for Education (MATHAI4ED) (2021)
Kulanin, E.D.: 3000 competitive math problems. Geometry, Ilex, Russia (2018)
Beklemishev, L.: Introduction to Mathematical Logic, Moscow State University Mehmat, pp. 44–48, Russia (2008)
JSXGraph Reference, current version available (2020). http://jsxgraph.uni-bayreuth.de/docs/symbols/JXG.Board.html
MathJax: Beautiful and accessible math in all browsers. https://www.mathjax.org/
Kurbatov, S.: Applications (2022). http://www.eia--dostup.ru/APP123.html. (in Russian)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Kurbatov, S.S., Fominykh, I.B. (2023). Complex Modeling of Inductive and Deductive Reasoning by the Example of a Planimetric Problem Solver. In: Kovalev, S., Sukhanov, A., Akperov, I., Ozdemir, S. (eds) Proceedings of the Sixth International Scientific Conference “Intelligent Information Technologies for Industry” (IITI’22). IITI 2022. Lecture Notes in Networks and Systems, vol 566. Springer, Cham. https://doi.org/10.1007/978-3-031-19620-1_43
Download citation
DOI: https://doi.org/10.1007/978-3-031-19620-1_43
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-19619-5
Online ISBN: 978-3-031-19620-1
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)