R.V. Dushkin¹

¹OOO "A-Ya ekspert" (Moscow, Russia)

²National Research Nuclear University MEPhI (Moscow, Russia) ¹drv@aia.expert

This paper proposes a systematic approach to constructing objects that can be used to represent basic mathematical concepts in combinatorial logic. In particular, we explore the use of Church numerals to describe numeric objects and then transfer them to a general algebraic structure. We also consider the possibility of expanding the object base by proposing methods for representing them using combinators of integer, rational, and complex numbers. The results of this study can be used to develop more accurate models and improve the processes of representing objects and logical inference on them within combinatorial logic. The overall goal of the paper is to propose a method for constructing objects to represent basic mathematical concepts in combinatorial logic, which can help in solving many mathematical problems. The method presented in this paper can also be used in other areas of mathematics and computer science where representation of mathematical objects is necessary. The novelty of this work lies in proposing a systematic and flexible method for constructing objects that allows representing basic mathematical concepts in combinatorial logic and can be used in other areas of mathematics and computer science. Furthermore, the method allows for expanding the object base, making it more universal and applicable in various contexts. The relevance of this article lies in the fact that combinatorial logic, as metamathematics, plays an important role in solving mathematical problems and in computer science research. This article will be useful and interesting to researchers and specialists in the fields of metamathematics, combinatorial logic, applied mathematics, and computer science. It can also be used for educational purposes, teaching undergraduate and graduate students the fundamentals of combinatorial logic and metamathematics.

Dushkin R.V. Attempt to systematically construct objects to represent basic mathematical concepts in combinatorial logic. Informationmeasuring and Control Systems. 2025. V. 23. № 5. P. 26−40. DOI: https://doi.org/10.18127/j20700814-202505-03 (in Russian)

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