Intuitionistic logic and it’s translations to other systems

In this paper, the author presents the system of intuitionistic logic in the form in which it appears in Brouwer and develops up to Heyting. It is contrasted with the concepts of classical calculus, and the main differences between these two approaches are highlighted. The paper also explores the relationship between these two logical systems, primarily by focusing on translation of the statements of classical logical calculus into intuitionistic calculus. Finally, an example of a similar translation of the modal calculus S4 into intuitionistic calculus is given, thereby delving into the area of the substructure of logical systems. In the conclusion, the author points out the philosophical relevance of researching the structure of logical systems in the search for a minimal basic system.