Translations of Network Languages

In this paper we describe new results of research on geometrical properties of complex control systems, the so-called Linguistic Geometry. This research includes the development of syntactic tools for knowledge representation and reasoning about large-scale hierarchical complex systems. It relies on the formalization of search heuristics of high-skilled human experts that have resulted in the development of successful applications in different areas. A hierarchy of subsystems of a complex system, the networks of paths, is represented as a hierarchy of formal languages. In this paper we investigate transformations of these networks while system moves from one state to another. The investigation consists of formal, constructive separation of changed and unchanged parts of system representation, the hierarchy of languages. Thus, we address the problem relative to the well-known Frame Problem for planning systems. A partial solution is presented in the form of the theorem about translations of network languages. Formal considerations are illustrated by example of Air Force robotic vehicles.