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Several principled measures of contextuality have been proposed for generalsystems of random variables (i.e. inconsistentlly connected systems). The firstof such measures was based on quasi-couplings using negative probabilities(here denoted by CNT3, Dzhafarov & Kujala, 2016). Dzhafarov and Kujala (2019)introduced a measure of contextuality, CNT2, that naturally generalizes to ameasure of non-contextuality. Dzhafarov and Kujala (2019) additionallyconjectured that in the class of cyclic systems these two measures areproportional. Here we prove that that conjecture is correct. Recently,Cervantes (2023) showed the proportionality of CNT2 and the Contextual Fractionmeasure (CNTF) introduced by Abramsky, Barbosa, and Mansfeld (2017). Thepresent proof completes the description of the interrelations of allcontextuality measures as they pertain to cyclic systems.

Measures of contextuality in cyclic systems and the negative probabilities measure CNT3