Formalization of inverse problems and its applications

We show how binary correspondences can be used for simple formalization of the notion of problem, definition of the basic components of problems, their properties, and constructions (the condition of a problem, its data and unknowns, solvability and unique solvability of a problem, inverse problem, composition and restriction of problems, etc.). We also consider topological problems and the related notions of stability and correctness. Particular attention is paid to problems with parameters. As an illustration, we consider a system of differential equations which describe a process in chemical kinetics, as well as the inverse problem.