A note on the relation between the Contextual Fraction and CNT2

Víctor H. Cervantes

doi:10.1016/j.jmp.2022.102726

A note on the relation between the Contextual Fraction and CNT₂

Víctor H. Cervantes

Psychology

Research output: Contribution to journal › Article › peer-review

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 (CNTF) 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 CNT₂, was proposed as one of the measures within the Contextuality-by-Default approach. In this note, I prove that CNTF=2CNT₂ within a class of systems, called cyclic, that have played a prominent role in contextuality research.

Original language	English (US)
Article number	102726
Journal	Journal of Mathematical Psychology
Volume	112
DOIs	https://doi.org/10.1016/j.jmp.2022.102726
State	Published - Feb 2023

Keywords

CNT
CNTF
Contextual fraction
Contextuality-by-Default
Measures of contextuality
Sheaf-theoretic contextuality

ASJC Scopus subject areas

General Psychology
Applied Mathematics

Online availability

10.1016/j.jmp.2022.102726

Library availability

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Cite this

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title = "A note on the relation between the Contextual Fraction and CNT2",

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 (CNTF) 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 CNT2, was proposed as one of the measures within the Contextuality-by-Default approach. In this note, I prove that CNTF=2CNT2 within a class of systems, called cyclic, that have played a prominent role in contextuality research.",

keywords = "CNT, CNTF, Contextual fraction, Contextuality-by-Default, Measures of contextuality, Sheaf-theoretic contextuality",

author = "Cervantes, {V{\'i}ctor H.}",

note = "The author carried out most of this work as an Illinois Distinguished Postdoctoral Researcher at the University of Illinois at Urbana-Champaign. The author is grateful to Sandra Camargo, Ehtibar Dzhafarov and an anonymous reviewer for feedback on earlier drafts, and to Ehtibar Dzhafarov and Giulio Camillo for fruitful conversations. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of the University of Illinois.",

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AB - 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 (CNTF) 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 CNT2, was proposed as one of the measures within the Contextuality-by-Default approach. In this note, I prove that CNTF=2CNT2 within a class of systems, called cyclic, that have played a prominent role in contextuality research.

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