An approach to the description of subject areas is proposed to solve constructive tasks in the form of constructive ontologies at the abstraction level of Cartesian closed categories. Constructiveness of ontology makes it possible correct automatic or automated (man-machine) construction of problem solving. In theory the ontology is constructed in such a way that it decides by itself tasks. The proposed paradigm is based on the paradigm of deductive synthesis of algorithms. The difference is that the synthesized algorithms are obtained as morphisms of the Cartesian closed category. In essence, ontology is designed to describe the subject area as a Cartesian closed category. In this case, initially objects of a category become what is traditionally thought of as classes of objects of a subject area. Elements of most of these classes themselves are often not considered at the initial stage. For constructiveness, the ontology is equipped with a logical machine for constructing output. This machine is conceived as an integral part of the most constructive ontology. From a practical point of view, it is important for reliability to have independent logical calculus and a derivation machine. These mechanisms control each other. The result of the logical machine is checked by calculus.
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