Observational Modeling of the KolmogorovSinai Entropy

In this paper, KolmogorovSinai entropy is studied using mathematical modeling of an observer $ Theta $. The relative entropy of a sub$ sigma_Theta $algebra having finite atoms is defined and then   the ergodic properties of relative  semidynamical systems are investigated.  Also,  a relative version of KolmogorovSinai theorem  is given. Finally, it is proved  that the relative entropy of a relative $ Theta $measure preserving transformations with respect to a relative sub$sigma_Theta$algebra having finite atoms is affine.