The present paper suggests separating the real structure of information systems and information about the system which subjects of the system have. The paper gives an example of such division using mathematical models of information security. The paper describes interaction processes between objects and the system that may result in changing their awareness structure. Based on the mathematical models described herein it is possible to establish which subjective images of the system are stable and define conditions that enable us to confirm that our own subjective image is objective. Problem setting for hiding some processes by modification of information stream structure in the system is provided.
Keywords -awareness structure, mathematic modeling, information security, informational restrictions, functional invisibilityI.