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The extended semantic realism (ESR) model proposes a new theoreticalperspective which embodies the mathematical formalism of standard (Hilbertspace) quantum mechanics (QM) into a noncontextual framework, reinterpretingquantum probabilities as conditional instead of absolute. We provide in thisreview an overall view on the present status of our research on this topic. Weattain in a new, shortened way a mathematical representation of the generalizedobservables introduced by the ESR model and a generalization of the projectionpostulate of elementary QM. Basing on these results we prove that theBell-Clauser-Horne-Shimony-Holt (BCHSH) inequality, a modified BCHSH inequalityand quantum predictions hold together in the ESR model because they refer todifferent parts of the picture of the physical world supplied by the model.Then we show that a new mathematical representation of mixtures must beintroduced in the ESR model which does not coincide with the standardrepresentation in QM and avoids some deep problems that arise from therepresentation of mixtures provided by QM. Finally we get a nontrivialgeneralization of the Luders postulate, which is justified in a special case byintroducing a reasonable physical assumption on the evolution of the compoundsystem made up of the measured system and the measuring apparatus.

Generalized Observables, Bell's Inequalities and Mixtures in the ESR Model for QM