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Standard derivations of the Bell inequalities assume a common-common-cause-system that is a common screener-off for all correlations and some additional assumptions concerning locality and no-conspiracy. In a recent paper (Graßhoff et al., The British Journal for the Philosophy of Science, 56, 663–680 (2005)) Bell inequalities have been derived via separate common causes assuming perfect correlations between the events. In the paper it will be shown that the assumptions of this separate-common-cause-type derivation of the Bell inequalities in the case of perfect correlations can be reduced to the assumptions of a common-common-cause-system-type derivation. However, in the case of non-perfect correlations a non-reducible separate-common-cause-type derivation of some Bell-like inequalities can be given. The violation of these Bell-like inequalities proves Szabó’s (International Journal of Theoretical Physics, 39, 911 (2004)) conjecture concerning the non-existence of a local, non-conspiratorial, separate-common-cause-model for a δ-neighborhood of perfect EPR correlations.

DOI: 10.1007/s11229-007-9198-1

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