relative model of the logical entropy of sub-σθ-algebras

In the context of observers, any mathematical model accord-ing to the viewpoint of an observer θ is called a relative model. the purpose of the present paper is to study the relative model of logical en-tropy. given an observer θ, we define the relative logical entropy and relative conditional logical entropy of a sub-σθ-algebra having finitely many atoms on the relative probability θ−measure space and prove the ergodic properties of these measures. finally, it is shown that the relative logical entropy is invariant under the relation of equivalence modulo zero.