Abstract
A general probability space is defined to be causally complete if it contains common cause type variables for all correlations it predicts between compatible variables that are causally independent with respect to a causal independence relation defined between variables. The problem of causal completeness is formulated explicitly and several propositions are presented that spell out causal (in)completeness of certain classical and non-classical probability spaces with respect to a causal independence relation that is stronger than logical independence.
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Gyenis, B., Rédei, M. (2011). Causal Completeness in General Probability Theories. In: Suárez, M. (eds) Probabilities, Causes and Propensities in Physics. Synthese Library, vol 347. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9904-5_7
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