In this paper we propose a theory of logically open systems. These lat
ter coincide with systems in metastable equilibrium with the environme
nt, in which the system-environment interaction cannot be described, a
s a principle, without taking into account the inner state of the syst
ems themselves. We introduce a particular hierarchy of these systems a
nd we prove some results relative to the limitations encountered when
dealing with them. We derive an undescribability principle which appli
es to logically open systems at the top of this hierarchy. Besides, we
suggest a strategy for coping with these Limitations and we sketch so
me possible applications of our theory to concrete cases. (C) 1998 Joh
n Wiley & Sons, Ltd.