The object of the study is text data processing in Ukrainian, including the creation and use of knowledge bases for logical reasoning and analysis of data consistency using ontology.
The purpose of the study is to fill the gaps in the currently available self-study resources by creating a recommendation system, in particular in the context of checking the accuracy and correctness of mathematical problems, enabling work with problems presented in Ukrainian, and automating the process of forming steps for solving problems.
Research methods used in the study: empirical and heuristic methods. Methods of mathematical logic, mathematical analysis, discrete mathematics, and functional programming. Additionally: methods of the systematic approach, including analysis, synthesis (structural, parametric) and decomposition.
Special methods are also used in the research work: tokenization, lemmatization, part-of-speech markup, and information extraction.
The scientific novelty of the results obtained in the thesis is as follows:
• for the first time, a method for extracting meaningful information from the texts of Ukrainian-language planimetry problems was developed, based on the frequency analysis of the collected planimetry problems and using natural language processing tools for Ukrainian to implement an automatic solving of Ukrainian-language planimetry problems;
• for the first time, a method of automatic verification of the correctness and consistency of the data that is obtained during the solving process of the problem and the data provided by the user, forming an internal representation of the problem’s solution as the construction of a term of type theory using the Lean functional programming language.
• for the first time, a method for automatic generation of steps for solving mathematical problems was built, that is based on logical inference obtained from the use of ontologies with the logical inference tools.
A recommendation system has been created that makes it possible to improve the efficiency of the educational process for pupils, applicants, students, teachers, and lecturers. In fact, a system has been developed that can automatically analyze the conditions of mathematical problems presented in Ukrainian and generate steps for solving them in a form that is understandable. This makes it possible to simplify and visualize the learning process and help avoid common mistakes when solving problems.
A method has been implemented that analyzes the text of the problem and uses the planimetry ontology. During the testing of the study results, it was shown that the average result of solving 50 planimetry problems by using large language models is 53.67 %, while the proposed recommendation system solves all 50 of these problems. Therefore, the proposed methods for extracting information from the text and applying the planimetry ontology provide almost twice as better solution to planimetry problems as currently available large language models.
There is also a method for correcting lemmatization errors in the Ukrainian language by using a dictionary, which helped to increase the final lemmatization accuracy by 1.66 %.
The use of ontologies and methods of logical inference allowed the system to check the obtained solutions for consistency, which is critical in the exact sciences. The implementation of a method using a functional programming language for these purposes ensured the correctness of the data.
Thus, the results of the study have practical application and can contribute to improve educational standards in Ukraine, increasing the number of high-quality mathematics solutions, and providing a tool to support users in the learning process.
The scientific and practical results of the research have been implemented in the educational activities of the Faculty of Informatics of the National University of Kyiv-Mohyla Academy, in particular at the Department of Multimedia Systems. In the future, the results of the dissertation are also planned to be implemented in the study of other disciplines to help deepen knowledge and analysis of automated systems by using the proposed recommendation system that can work with Ukrainian-language texts of mathematical problems, solve them independently and help end users to solve them.
