A Hilbert space realization of nonlinear quantum mechanics as classical extension of its linear counterpart

This paper studies the state-effect-probability structure associated with the quantum mechanics of nonlinear (homogeneous, in general nonadditive) operators on a Hilbert space. Its aim is twofold: to provide a concrete representation of the features of nonlinear quantum mechanics on a Hilbert space, and to show that the properties of the nonlinear version of quantum mechanics here described have the structure of a classical logic.