Decision making modes and open systems

The study describes a method for representing open systems. Thus, and especially for decision processes, two points of view are alternatively used : - The first one connected to an outside observer, is rigorous and corresponds to closure phases. This point of view is represented by an arithmetic language, whose tools are arithmetic relators. - The second one, connected to an inside observer, is intuitive, corresponds to opening phases and involves heuristics linked to the previous language. The method is applied to an example from physics and some further developments to other fields are outlined.