This paper discusses the problem of applying the "Unit-Function-Object" system-object approach to conceptual systems. The results of a comparative analysis of the material systems are presented, i.e., phenomena (systems phenomena) and conceptual systems, i.e., classes (system-classes). A universal definition of the "system" concept has been developed that consider both types of systems. Variants of the formal description of the system class are proposed using the apparatus of calculus of objects and descriptive logic. It is shown that a number of known system-wide laws apply to material systems, i.e., systems-phenomena as well as conceptual systems, i.e., system-classes. The presented results substantiate the possibility of including system-classes on par with systems-phenomena in the theory of systems based on the systemobject approach. In addition, the results make it possible to improve the existing and create new classification systems, which are an important type of conceptual model of conceptual knowledge, as conceptual models that take system-wide regularities into account become models that reflect the systemic nature of actual reality.

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The nature of information (conceptual) systems is studied using a system-object approach. The conclusion is made that the hierarchies of conceptual and material systems are an object-oriented system, whose conceptual systems are external systems (class systems) that determine the properties of specific objects, and objects-material or internal systems (systems-phenomena) that perform real interactions. The results of a formal description of the hierarchy of conceptual systems are considered, taking their interconnection into account by formalization using descriptive logic of some provisions of the system-object approach. The syntax and semantics of the ALCOIQ descriptive logic and its extension to the SHOIQ logic are described. The SHOIQ logic is introduced; it formally describes the concepts of the volume and content of a conceptual system that expand system theory based on a system-object approach.

This article is devoted to the main problems in the one of the most actual research area in knowledge managementontology engineering. An original approach to solving the problems of applied ontologies building, inference on them, ontology mapping and merging, which is based on the "Unit-Function-Object" approach, is proposed. The main components of the corresponding methods with the basis of UFO approach and UFO domain modeling principles are considered.

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