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arXiv:1511.02823 · Journal of Mathematical Psychology

Negative probabilities and contextuality

J. Acácio de Barros, Janne V. Kujala, Gary Oas

Published May 31, 2016• 26 citations
arXivHTMLPDF
DOI
10.1016/j.jmp.2016.04.014

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Several principled measures of contextuality have been proposed for general systems of random variables (i.e. inconsistentlly connected systems). The first of 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 a measure of non-contextuality. Dzhafarov and Kujala (2019) additionally conjectured that in the class of cyclic systems these two measures are proportional. Here we prove that that conjecture is correct. Recently, Cervantes (2023) showed the proportionality of CNT2 and the Contextual Fraction measure (CNTF) introduced by Abramsky, Barbosa, and Mansfeld (2017). The present proof completes the description of the interrelations of all contextuality measures as they pertain to cyclic systems.