Meta- and hypergraph representations allow reducing the amount of processed data without losing the original information. This advantage determines the most promising area for their application: the problems of big data analysis, provided that this data can be described using a graph representation. The article proposes an approach to modeling hierarchical systems based on nested metagraphs. Category theory is used to eliminate ambiguity in the interpretation of concepts. Formalized descriptions of static and dynamic nested metagraphs, methods for defining them, as well as basic operations are given. The basis of concepts, nested metagraphs is a monoid, as an information object, which is characterized by an internal form, internal and external contents. Thus, a monoid is a generalization of a graph structure and is interpreted as a vertex of a generalized graph.

Keywords: nested metagraph, metagraph monoid, metagraph adjacency matrix, operations on nested metagraphs

The article considers the possibility of constructing a formal negotiating model of the principal-agent, used to predict the behavior of subjects in the case of intra-firm management. To build such a model, we consider a number of necessary conditions and principles for the relationship between the principal and the agent, such as the common goal and various interests, the project is the interaction subject, the agents are active and form the maximum coalition, interaction and cooperation of principal and agents are based on democratic management style and collegial decision-making under uncertainty.

Keywords: organizational system, principal agent, negotiations, behavior modeling, OS goal, coordination of actions, resource theory, firm theory, incentive problem, contract theory, project life cycle, decision making uncertainty, maximum coalition of agents

Peculiarities mechanisms predict and evaluate the results of actions of an intelligent agent. Building and planning procedures and correction strategy and tactics based on the behavior of a cybernetic circuit functional systems. This scheme is a concept of an intelligent agent architecture.

Keywords: Intelligent agent, adaptive behavior, the model achieve the goal, the efferent mechanism synthesis

"The concept of the nested metagraph as the model of a complex object with different levels of generalization is introduced. It is shown that the nested metagraphs reflect the general system concept for description of complex objects with synergistic effect. This approach enables moving from the set-theoretic description of complex objects to their algebraic-theoretic description, thus increasing the model adequacy to real-life objects. The application of the nested metagraphs, in particular to business-intelligence and semantic search is considered. "

Keywords: nested metagraphs, complex object, hyperedge as the essence, business analysis, a semantic network