Quasi-commutative diagrams of multiresolutional systems for representation and control

The multiresolutional approach for representation of intelligent systems with NIST-RCS Architecture leads to a number of mathematical problems related to categorical models associated with the multiresolutional representation. One of these problems is investigation of quasi-commutative diagrams that are mathematical formalization of relations between levels of multiresolutional representation. All levels in the multiresolutional representation of an intelligent system are representations of this system with different values of resolution. Relations between different levels of the representation are expressed by functors between the categories of the representation. This dependency is associated with morphisms in the categories of representation that correspond to different levels of resolution. This association is expressed by diagrams. This paper is focused upon the mathematical formalization of the problem of synthesis of a behavior generator of high level with quasi-commutative diagram of control for given restricted behavior morphism of low level.