The architecture of a qualitative cognitive agent is proposed, which includes: the knowledge representation model, the behavioral planning and agent cooperation subsystem. The agent knowledge model is represented in the form of a qualitative conceptual framework structuring the agents functioning environment on the subspaces defining the classes of possible states. In the agent behavior planning subsystem, the agent's choice of action is based on solving the inverse problem in the logical-linguistic equations of agent dynamics. The subsystem of agent cooperation is based on the criterion of mutual usefulness of agents. The proposed architecture of a qualitative cognitive agent allows implementing and exploring various principles of command behavior of set agent with a BDI-architecture with less labor, while maintaining the basic properties of intelligent agents.