Relative model of the logical entropy of sub-\sigma_\Theta-algebras

‎In the context of observers‎, ‎any mathematical model according to the viewpoint of an observer \Theta is called a relative model‎. ‎The purpose of the present paper is to study the relative model of logical entropy‎. ‎Given an observer \Theta ‎, ‎we define the relative logical entropy and relative conditional logical entropy of a sub- \sigma_\Theta -algebra having finitely many atoms on the relative probability \Theta‎- ‎measure space and prove the ergodic properties of these measures‎. ‎Finally‎, ‎it is shown that the relative logical entropy is invariant under‎‎the relation of equivalence modulo zero.

کلیدواژه ها:

Observer‎ ، ‎Relative logical entropy‎ ، ‎sub- \sigma_\Theta -algebra ، invariant