In this work, the goal is to develop a model of conversation system that would be able to acquire knowledge on its own, learning in a dialogue with a person. The implementation of the project lies in an interdisciplinary area including didactics, linguistics and natural language processing, and, in our opinion, the results will have important theoretical and practical significance for each field of science. The idea of the project is creating the intelligence core for the Self-Learning Conversational Agent (SLCA) that acquires knowledge through reinforcement learning using natural didactic models in the dialogue with a person in a natural language. The solution of the set tasks lies at the intersection of artificial intelligence and machine learning methods with linguistic methods of discourse analysis and text synthesis by means of a language of meanings. As a case-study we offer to consider learning a foreign language learning due to the challenges of rapid mastering it and improving and maintaining skills in its usage which are still unsolved.