  In quantum physics, the notion of contextuality has a variety of
interpretations which are typically associated with the names of their
inventors, say Bohr, Bell, Kochen and Specker, and recently Dzhafarov. In fact,
Bohr was the first who pointed to contextuality of quantum measurements as a
part of formulation of his principle of complementarity. (Instead of
"contextuality", he considered dependence on "experimental conditions.")
Unfortunately, the contextuality counterpart of the complementarity principle
was overshadowed by the issue of incompatibility of observables. And the
interest for contextuality of quantum measurements rose again only in
connection with the Bell inequality. The original Bohr's contextuality, as
contextuality of each quantum measurement, was practically forgotten. It was
highlighted in the works of the author of this paper, with applications both to
physics and cognition. In this note, the theory of open quantum systems is
applied to formalization of Bohr's contextuality within the the scheme of
indirect measurements. This scheme is widely used in quantum information theory
and it leads to the theory of quantum instruments (Davis-Lewis-Ozawa). In this
scheme, Bohr's viewpoint on contextuality of quantum measurements is
represented in the formal mathematical framework.
