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I think You use the different concept of the probability theory than me. You say that in CH approach the time symmetric formulation of probability is used. OK, but in my concept of the probability theory this is impossible, since in my concept of the probability theory the evolution is strictly uni-directional. It is clear that we use different concepts of the probability theory. I think this is the point.
But nevertheless, there are similarities. In the extended theory of probability, the basic concept is the concept of a context. The context is a maximal set of mutually compatible events. In each context the extended probabiity is reduced to the standard probability. Each experiment must be associated with certain context: only events from this context can be observed in a given experiment. Thus the context can be understood as an analog of your framework. But I need much more time to study the CH approach.