  We develop the contextual measurement model (CMM) which is used for
clarification of the quantum foundations. This model matches with Bohr's views
on the role of experimental contexts. CMM is based on contextual probability
theory which is connected with generalized probability theory. CMM covers
measurements in classical, quantum, and semi-classical physics. The CMM
formalism is illustrated by a few examples. We consider CMM framing of
classical probability, the von Neumann measurement theory, the quantum
instrument theory. CMM can also be applied outside of physics, in cognition,
decision making, and psychology, so called quantum-like modeling.
