{"title":"A note on the relation between the Contextual Fraction and CNT2","authors":"Víctor H. Cervantes","doi":"10.1016/j.jmp.2022.102726","DOIUrl":null,"url":null,"abstract":"<div><p>Contextuality (or lack thereof) is a property of systems of random variables. Among the measures of the degree of contextuality, two have played important roles. One of them, Contextual Fraction (<span><math><mtext>CNTF</mtext></math></span>) was proposed within the framework of the sheaf-theoretic approach to contextuality, and extended to arbitrary systems in the Contextuality-by-Default approach. The other, denoted <span><math><msub><mrow><mtext>CNT</mtext></mrow><mrow><mn>2</mn></mrow></msub></math></span>, was proposed as one of the measures within the Contextuality-by-Default approach. In this note, I prove that <span><math><mrow><mtext>CNTF</mtext><mo>=</mo><mn>2</mn><msub><mrow><mtext>CNT</mtext></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span> within a class of systems, called cyclic, that have played a prominent role in contextuality research.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"112 ","pages":"Article 102726"},"PeriodicalIF":2.2000,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Psychology","FirstCategoryId":"102","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022249622000645","RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 1
Abstract
Contextuality (or lack thereof) is a property of systems of random variables. Among the measures of the degree of contextuality, two have played important roles. One of them, Contextual Fraction () was proposed within the framework of the sheaf-theoretic approach to contextuality, and extended to arbitrary systems in the Contextuality-by-Default approach. The other, denoted , was proposed as one of the measures within the Contextuality-by-Default approach. In this note, I prove that within a class of systems, called cyclic, that have played a prominent role in contextuality research.
期刊介绍:
The Journal of Mathematical Psychology includes articles, monographs and reviews, notes and commentaries, and book reviews in all areas of mathematical psychology. Empirical and theoretical contributions are equally welcome.
Areas of special interest include, but are not limited to, fundamental measurement and psychological process models, such as those based upon neural network or information processing concepts. A partial listing of substantive areas covered include sensation and perception, psychophysics, learning and memory, problem solving, judgment and decision-making, and motivation.
The Journal of Mathematical Psychology is affiliated with the Society for Mathematical Psychology.
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