С быстрым развитием технологий компьютерное обучение все больше интегрируется с методами искусственного интеллекта с целью разработки более персонализированных образовательных систем. Такие системы известны как интеллектуальные обучающие системы (ИОС). Рассматривается возможность применение логических методов для расширения функционала ИОС. Предлагается метод автоматического получения решения упражнений средствами дедукции языка L. Предлагается метод автоматической генерации упражнений по заданной спецификации средствами абдукции языка L.

The paper is devoted to studying the stability of complex systems, which include diversified and heterogeneous elements. In order to analyze the stability of such systems, it is proposed to develop the process of dynamic determination of the main factors. For this purpose, this paper uses a variant of cognitive modeling based on the concept of “influence”. The proposed approach implies, in a sense, a broader view of the concept of the “fuzzy cognitive map” introduced by B. Kosko. “Influence” does not mean “causality”, allows a broader interpretation range, and is calculated in a special way that makes it possible to prove rigorous theorems. A complex system is represented as a digraph, and the selection of the main factors is proposed to be based on the concept of “influence”, which is introduced as follows. All nodes of the graph are assigned an abstract property “significance”, which allows you to compare heterogeneous factors, and a particular computational procedure is introduced that allows this “significance” to be calculated. The “influence” of factors on each other is defined as a mathematically formalized response in accordance with the introduced computational procedure of the “significance” of the studied factor to the variation in the “significance” of input factors. For example, the analysis of the sustainability of a large-scale model of the Russian economy in terms of the strength of the “influence” is provided.

The high rates of the scientific and technical process have made significant adjustments to the methods for assessing the country’s GDP, labor productivity, and the number of the economically active population. Industry 4.0 has fundamentally changed the structure of the labor market and employment of the population in all countries, presenting new requirements for employers and employees. The use of self-driving vehicles, robots, automation of most business processes in various sectors of the national economy significantly increases labor productivity, ensures GDP growth, and reduces employment. Industry 4.0 makes available new, digital formats for continuous professional development, making it possible to adapt educational content to personnel and enterprise management quickly. A mathematical model was developed to predict the significant indicators of the economy and the labor market. It is a linear equation system that, given the initial conditions, provides the formation of various forecast scenarios. The results of computational experiments on calculating labor productivity, changes in the number of employees and earnings, as well as the number of the economically active population of the Russian Federation in 2021-2035, are presented. The calculations were carried out for three main combinations: a) changes in GDP; b) changes in labor productivity c) changes in numbers. The research’s information base is the state statistical sources and forecasts both in general and individual enterprises.

This paper considers the technological core model of an economic system and mathematical methods of its analysis. As a formalized criterion for the effectiveness of structural innovations, an indicator of productivity is proposed. The problem of finding an equilibrium state that optimizes the productivity of the technological core of the economy is formally stated. The method of equivalent transformation of the model considering the achieved value of indicators is developed. Several propositions on the properties of the equilibrium state are proved. A multi-stage process for calculating the trajectory that brings the economic system closer to the equilibrium state is constructed. The developed model uses the intersectoral balance of national accounts of the economy. The model is analyzed by determining the preferred structure of outputs at the development stages of the economic system’s technological core. The phased process of changing the structure of outputs that asymptotically brings the technological core to the productivity maximum is calculated on an example of Russia’s data. The results allow assessing the potential growth of economic productivity within the existing technological order by eliminating structural disproportions.

Получена локальная нормальная форма для векторных полей Руссари с вырожденной квадратичной частью.