In this chapter we develop the contextual approach to quantum mechanics.This approach matches with the views ofBohr who emphasized that the quantum description represents complexes ofexperimental physical conditions, in the modern terminology – experimentalcontexts. In this chapter we formalize the contextual approach on the basisof contextual probability theory which is closely connected with generalizedprobability theory (but interpretationally not identical with it). The contextualprobability theory serves as the basis of the contextual measurementmodel (CMM). The latter covers measurements in classical, quantum, andquasi-classical physics.

In this chapter the contextual measurement model (CMM) is employed forprobabilistic structuring of classical and quantum physics. We start with CMM framing of classical probability theory (Kolmogorov 1933) servingas the basis of classical statistical physics and thermodynamics. Then weconsider the von Neumann quantum measurement theory with observablesgiven by Hermitian operators and the state update of the projective typeand represent it as CMM. The quantum instrument theory is a generalizationof the von Neumann theory permitting state updates of the non-projectivetype and it also can be represented as CMM. We also show connectionof the generalized probability theory with the space of probability measureswith CMM. Finally, linear space representation for contextual probabilityspace is constructed by using the construction going back to Mackey.