The interpretation of the violation of Bell-Clauser-Horne inequalities is
revisited, in relation with the notion of extension of QM predictions to
unmeasurable correlations. Such extensions are compatible with QM predictions
in many cases, in particular for observables with compatibility relations
described by tree graphs. This implies classical representability of any set of
correlations , , , and the equivalence of the
Bell-Clauser-Horne inequalities to a non void intersection between the ranges
of values for the unmeasurable correlation associated to different
choices for B. The same analysis applies to the Hardy model and to the "perfect
correlations" discussed by Greenberger, Horne, Shimony and Zeilinger. In all
the cases, the dependence of an unmeasurable correlation on a set of variables
allowing for a classical representation is the only basis for arguments about
violations of locality and causality.Comment: Some modifications have been done in order to improve clarity of
presentation and comparison with other approache
