The Analysis and the Adaptive Correction of Learning Trajectories With the Help of Agents

This paper proposes a novel architecture of a multi-agent system and its formal specification for analyzing and adaptively correcting students' learning trajectories using software agents in digital learning environments. The proposed approach integrates artificial intelligence tools, tem- poral logic, and a multi-agent system architecture to ensure personalized adaptation of educational content. The main objective is to create a system capable of automatically collecting data on students' academic activities, analyzing this data using machine learning techniques, and gene- rating and evaluating individual recommendations. These recommendations can include partic- ipation in group studies, additional consultations, or enrolling in advanced courses depending on the students’ performance dynamics. The proposed system model also includes metrics for eva- luating the system's effectiveness, such as improved academic performance, increased engagement, reduced reaction time to difficulties, and student satisfaction. Neural network-based prediction is used to detect trends or deviations in students' learning patterns, which serve as the basis for dynamic adaptation of their learning path. The system uses Python and Keras frameworks to implement the analytical core, while monitoring and feedback mechanisms ensure real-time re- sponsiveness. The proposed system model also includes metrics for evaluating the system's effect- tiveness, such as improved academic performance, increased engagement, reduced reaction time to difficulties, and student satisfaction. Experimentally, the system was tested on a simulated student group studying “Parallel and Distributed Computing”, with results indicating measurable impro- vement in performance and motivation. The study demonstrates that the use of intelligent software agents can enhance personalization in education and support students more effecttively. Future work may include deeper analysis of emotional and social factors, ethical considerations of AI- based decision-making, and large-scale deployment in institutional LMS platforms.