Contextual measurement model and quantum theory

We develop a contextual measurement model (CMM) that is used for the clarification of the quantum foundations. This model matches Bohr's views on the role of experimental contexts. CMM is based on a contextual probability theory that 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 the CMM framing of classical probability, the von Neumann measurement theory and the quantum instrument theory. CMM can also be applied outside of physics, e.g. in cognition, decision-making and psychology, the so-called quantum-like modelling.