On the relation between the probabilistic characterization of the common cause and Bell׳s notion of local causality

• Local causality is defined in the isotone net framework borrowed from AQFT.
• Local causality implies probabilistic common cause equations (modulo no-conspiracy).
• Local causality does not imply the existence of non-atomic common causes.
• Probabilistic common causes can be localized in the weak past.
• A weak common cause can be genuine only if it contains a built-in correlation.

In this paper the relation between the standard probabilistic characterization of the common cause (used for the derivation of the Bell inequalities) and Bell׳s notion of local causality will be investigated in the isotone net framework borrowed from algebraic quantum field theory. The logical role of two components in Bell׳s definition will be scrutinized; namely that the common cause is localized in the intersection of the past of the correlated events; and that it provides a complete specification of the ‘beables’ of this intersection.