МЕТОД АЛГЕБРО-ЛОГІЧНОГО МОДЕЛЮВАННЯ ПРЕДМЕТНИХ ГАЛУЗЕЙ ДЛЯ СИСТЕМ ВИДОБУВАННЯ ЗНАНЬ

The subject of this study is the use of algebraic-logical modeling to develop adaptive distance learning systems. The proposed model is based on knowledge graphs, where each node represents a learning topic, and edges define logical and semantic relationships between subject areas. This approach enables the automation of determining the sequence of material acquisition and adapting the learning trajectory to the student's knowledge level. The objective of this work is to create a formal mathematical model of an adaptive learning process that ensures a personalized selection of learning topics and automatic adjustment of the learning trajectory based on student performance. The proposed model employs an ontological approach to structuring learning content and predicate algebra to define transition rules between topics. To achieve this goal, the following tasks were completed: an analysis of modern adaptive learning systems was conducted, a knowledge graph was developed to automate learning trajectories, an adaptive testing mechanism was implemented, and a software system for graph visualization was created. An essential aspect of the implementation is the use of WPF and QuickGraph for the interactive construction and processing of the educational trajectory. The methods considered include finite predicate algebra, graph theory, and object-oriented programming. Special attention is given to automated knowledge graph visualization and methods for adapting the learning process using logical equations. Results. An adaptive learning process model was obtained, allowing for a formal description of the structure of educational dependencies and ensuring the automatic selection of subsequent topics based on the student’s knowledge level. A software system for constructing and visualizing a knowledge graph in .NET (WPF) was implemented. The proposed approach provides learning process personalization, automated testing, and student progress analysis. The conclusions highlight the advantages of the developed model, including its integration into modern distance learning platforms and its potential to improve learning efficiency through dynamic testing and educational trajectory analysis.