In the paper the problem of formalization and identification of real and virtual information objects and traceability of their relations in the studied subject domain using the rules of monomorphism and polymorphism of the mathematical theory of sets and categories is investigated. According to the principles of the systems engineering standard ISO/IEC 15288 models and methods of analytical software creation are developed. It is shown that the structure of such analytical software meets the conditions of Cartesian closed logic that considerably expands the range of tasks, which can be solved using this software. This is made possible because the effective reengineering of the software can be carried out in real time mode without any changes of its program code. The formalized description of the relations between virtual and real objects using the rules of data storages is offered. The method of creation of Chomsky hierarchies and a method of Osgood's semantic differentials are applied. As an example the structure of the distributed analytical software of the talent pool management of the industrial enterprise formed together with educational institutions of the higher education is considered.
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