About the ontology of task types and methods of their solution

The article develops the version of the transdisciplinary approach proposed at the V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences focused on identifying and systematizing the types of tasks and methods for their solution. This approach starting from the task, as such, ascends inductively from the concept of the task through the concept of the single to the Universal, then allowing deductively identify and systematize the types of singles, establishing the place of tasks in this construction. The possibility of identifying and systematizing the types of tasks that are qualitatively different in methods of solution, based on the sources that generate these tasks, is considered. A procedure for identifying and systematizing key types of tasks is presented, on which any other tasks can be decomposed. In accordance with the decomposition procedure, the methods and properties of methods for solving key tasks determine the methods and properties of methods for solving tasks combined on their basis. The consistency of the proposed way of systematization with the known ontological constructions follows from the inductive-deductive procedure for tracing the sources of the foundations of concepts and provisions underlying various ontological constructions. This makes it possible to determine the place of the mentioned foundations in the formed integral picture of the types of singles, types of tasks and methods from the solution, and hence the place in this picture of the considered ontological constructions. Potential capabilities opened up on the way of further following the transdisciplinary approach are revealed; the directions of further research are indicated, allowing in the future to develop an extremely formalizable technology for the synthesis of methods for solving various problems.