Formalization of system-object method of knowledge representation by calculation of systems as functional objects

• Published in: Journal of physics. Conference series 2021-02, Vol.1801 (1), p.12025
• Main Authors: Zhikharev, A G, Matorin, S I, Tinyakov, O A, Shcherbinina, N V, Migal, L V
• Format: Article
• Language: English
• Subjects: Algorithms; Context; Knowledge representation; Mathematical analysis; Operators (mathematics); Optimization; Physics
• ISSN: 1742-6588; 1742-6596
• DOI: 10.1088/1742-6596/1801/1/012025

The paper considers some elements of the calculation systems as functional objects. The formal foundations of calculus of systems proposed by the authors were preceded by research on the development of a mathematical apparatus that allows formalizing the procedures for developing system-object simulation models of processes and systems. In the work, the previously developed formal apparatus is supplemented by the context operator, and some theorems related to the structural and functional characteristics of the modeled objects are formulated and proved. In particular, using the context operator, the statement is proved that the connection of a nodal object with the external environment generates the same connections of other nodal objects whose functions are realized due to the functions of the first nodal objects. It is shown that this statement is true for both incoming and outgoing connections with respect to a nodal object. Intrasystem connections are considered that are also capable of generating connections for their contextual node objects. In addition, the paper proposes a new formal record of the function of a nodal object for a situation when it is implemented due to the functions of other nodal objects. The proposed formalisms are considered on the example of a system-object model of an abstract system. In the future, based on the calculus of systems, optimization algorithms for system-object simulation models will be formulated according to various optimization criteria.