DOI: 10.25136/2644-5522.2018.3.26613

Abstract: The object of research in this article are methods used to solve problems of designing control systems for complex technological complexes. The development of the theoretical basis for the creation of such methods is based on system analysis and is an important scientific problem. One approach to solving this problem is to develop a universal formalism that will be used to describe a variety of technologies. The choice of the mathematical apparatus determines the very possibility of solving this problem. In addition, the choice of the mathematical apparatus depends on the toolkit with which the user will have to work. In this paper, it is proposed to create mathematical models, methods, and to establish connections using the mathematical theory of categories.The main conclusions of this work are the following:1. The tasks of mapping semantics and the logic of concepts can be solved using methods of mathematical category theory.2. A unified description of families of heterogeneous mathematical models that reflect a different level of abstraction (generalization) at the stage of infologic modeling makes it possible to create formulations for the general definition of models with a description of their structure.

DOI: 10.25136/2644-5522.2017.3.23087

Abstract: This article is devoted to the the methods used in the theory of Сomputer-Assisted Design. Development of a theoretical framework of technologies of the automated designing is an important scientific problem. One of directions employed to solve this problem is its reduction to a single universal formalism used for describing a variety of technologies, which will be appropriate for the design of complex heterogeneous systems for integration and coordination of these technologies. The solution to this problem depends on the choice of the mathematical apparatus. In this article the author proposes creation of the computer-aided design methods using mathematical category theory. The author then discusses methods for the formation of a mathematical apparatus for CAD based on the mathematical category theory in order to establish mathematical models and the correlations between them at different levels of abstraction. It is shown that the formulation of regularities in the mapping from conceptual view the conceptual view of the subject objectives the basic reasons are: a consistent mathematical apparatus of formation models;  an uniform structure of the regularities of formation models; existence of the laws of cyclicality. Pattern display models of conceptual representation in the model conceptual representation of the subject is the identity in the application of functional abstractions for dynamic and static components during the process of formation (establishment) of the relations between them and the identity of the models on the same level of abstraction with the same view.