Kolmogorovian Censorship, Predictive Incompleteness, and the locality loophole in Bell experiments

In the foundations of quantum mechanics, the Kolmogorovian Censorship (KC) stipulates that quantum probabilities can be identified with classical, Kolmogorovian probabilities when considering a specified measurement context. Then in any given measurement context it is possible to build a Kolmogorovian probability distribution, or equivalently a hidden variable theory; however this distribution must be matched to the chosen context. In a loophole-free Bell test, the remote random choices of measurements (polarizers orientations) have the purpose to prevent that this matching can be obtained from any relativistically causal transmission between the source and the detectors. Then the matching (required to violate Bell's inequalities) may be obtained either by an instantaneous influence at a distance between the source and the detectors (explicit nonlocality), or by assuming that it is pre-established before the actual experiment takes place (super-determinism). If both influence at a distance and super-determinism are not accepted on physical grounds, a third way is still available, called "predictive incompleteness": it tells that the usual quantum state is incomplete, as long as the measurement context has not been specified. In agreement with the general quantum framework called CSM (Contexts, Systems and Modalities) we argue that predictive incompleteness is the correct quantum way to understand the violation of Bell's inequalities.