Contextual inferences, nonlocality, and the incompleteness of quantum mechanics

It is known that "quantum non locality", leading to the violation of Bell's inequality and more generally of classical local realism, can be attributed to the conjunction of two properties, that we call here elementary locality and predictive completeness. Taking this point of view, we show again that quantum mechanics violates predictive completeness, allowing to make contextual inferences, which can in turn explain why quantum non locality does not contradict relativistic causality. But if the usual quantum state $\psi$ is predictively incomplete, how to complete it ? We give here a set of new arguments to show that $\psi$ should be completed indeed, not by looking for any "hidden variables", but rather by specifying the measurement context, which is required to define actual probabilities over a set of mutually exclusive physical events.