Annotation: The article is devoted to the improvement of the information support system of decision-making processes by operators of the air traffic automated control system. The apparatus of knowledge base formalization of the subject domain was proposed, based on the basic factors of the categories theory and the existence calculus. It is proposed to present structures for description of objects with the help of objectives system. Axioms are formed based on the network model of tasks and objectives for each of the subtasks and the type of theory. The basis for their construction is the semantic network presentation of the object and the formulas of separate subobjects. Each presentation of the object in the theory of physical reality is mapped to the correspondence of the aggregate of information converters, which transform information about the original concepts that satisfy the initial conditions, into information about the resulting concepts that must meet the new conditions. As a result, the proposed formalization apparatus allows the synthesis of programs to solve decision-making support tasks.