Distinction between the concepts of mathematical and logical modeling

Abstract

Introduction. Technologies of mathematical and logical modeling of problem solving according to the existing practice of their distribution are divided into two areas: widespread mathematical modeling and infological modeling which is currently underdeveloped, especially for sophisticated systems. Fundamental differences between these technologies, in particular for the machining preproduction, are that logical modeling is informationally and logically related to organization systems, and mathematical modeling is associated with control processes in the organization systems. Logical modeling is used to operate with geometric objects in the technological schemes of their interaction through basing methods, geometric shaping in a static (ideal) setting of the corresponding schemes. Mathematical simulation is used to operate material objects in the control processes of their transformations through cutting methods, i.e. imperfectly, considering heterogeneous errors. Between the organization systems under study and management processes in them, there are information and logical links of their organic unity, which deny their separate consideration. In the information deterministic technology for solving problems of a high-level automation, the distinction between the concepts of “mathematical” and “logical” modeling is relevant; it has scientific novelty and practical significance.Materials and Methods. To characterize the properties of the concepts of “mathematical modeling”, “logical modeling” and the knowledge functions resulting from the formulation of these concepts, fundamentally different methods and appropriate tools are used. The differentiation of the concepts under consideration is based on the differentiation of technologies (methods, appropriate tools, algorithms, operations) for solving applied problems of any knowledge domain.Research Results. The ideas of “logical modeling” and “mathematical modeling” are conceptual general-theoretical notions with invariant properties required for solving practical problems of any application domain. In accordance with the distinction between these concepts, the problem solving technologies are divided into two types: system engineering technology – in the organization of information object systems, and system science – in the management processes of transformation of the corresponding material objects. These areas should exist in the information and logical link of their organic unity.Discussion and Conclusions. The author distinguishes between the concepts of “logical modeling” and “mathematical modeling”, which is a key condition for a successful transition to the deterministic information technology of a high-level automation in solving practical problems of any knowledge domain, for example, of the production design machining