Several principled measures of contextuality have been proposed for general systems of random variables (i.e. inconsistently connected systems). One such measure is based on quasi-couplings using negative probabilities (here denoted by CNT 3 , Dzhafarov & Kujala, 2016 Quantum interaction ). Dzhafarov & Kujala (Dzhafarov & Kujala 2019 Phil. Trans. R. Soc. A 377 , 20190149. ( doi:10.1098/rsta.2019.0149 )) introduced a measure of contextuality, CNT 2 , that naturally generalizes to a measure of non-contextuality. Dzhafarov & Kujala (Dzhafarov & Kujala 2019 Phil. Trans. R. Soc. A 377 , 20190149. ( doi:10.1098/rsta.2019.0149 )) additionally conjectured that in the class of cyclic systems these two measures are proportional. Here we prove that conjecture is correct. Recently, Cervantes (Cervantes 2023 J. Math. Psychol . 112 , 102726. ( doi:10.1016/j.jmp.2022.102726 )) showed the proportionality of CNT 2 and the Contextual Fraction measure introduced by Abramsky & Brandenburger (Abramsky & Brandenburger 2011 New J. Phys . 13 , 113036. ( doi:10.1088/1367-2630/13/11/113036 )). The present proof completes the description of the interrelations of all contextuality measures proposed within or translated into the Contextuality-by-Default framework so far as they pertain to cyclic systems. This article is part of the theme issue ‘Quantum contextuality, causality and freedom of choice’.

中文翻译：

---

循环系统中的上下文测量和负概率测量 CNT 3

对于一般的随机变量系统（即不一致连接的系统），已经提出了几种原则性的上下文相关性度量。其中一种措施是基于使用负概率的准耦合（此处表示为 碳纳米管 3 ，扎法罗夫和库贾拉，2016量子相互作用）。扎法罗夫与库亚拉 (扎法罗夫与库亚拉 2019菲尔. 跨。R.苏克。A 第377章，20190149。（doi:10.1098/rsta.2019.0149)) 引入了上下文相关性的衡量标准， 碳纳米管 2 ，这自然可以概括为非上下文性的度量。扎法罗夫与库亚拉 (扎法罗夫与库亚拉 2019菲尔. 跨。R.苏克。A 第377章，20190149。（doi:10.1098/rsta.2019.0149)) 另外推测在循环系统类中这两个度量是成比例的。这里我们证明猜想是正确的。最近，塞万提斯 (Cervantes 2023J.马斯。心理学。112，102726。（doi:10.1016/j.jmp.2022.102726)) 显示了比例 碳纳米管 2 以及 Abramsky 和 ​​Brandenburger 引入的上下文分数度量 (Abramsky & Brandenburger 2011新物理学杂志。13，113036。（号码：10.1088/1367-2630/13/11/113036））。本证明完成了对在默认上下文框架中提出或翻译成的所有上下文度量的相互关系的描述，只要它们涉及循环系统。本文是“量子背景、因果关系和选择自由”主题的一部分。