# A note on the relation between the Contextual Fraction and CNT2

@inproceedings{Cervantes2021ANO, title={A note on the relation between the Contextual Fraction and CNT2}, author={V{\'i}ctor H. Cervantes}, year={2021} }

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…

## References

SHOWING 1-10 OF 39 REFERENCES

Measures of contextuality and non-contextuality

- Mathematics, PhysicsPhilosophical Transactions of the Royal Society A
- 2019

We discuss three measures of the degree of contextuality in contextual systems of dichotomous random variables. These measures are developed within the framework of the Contextuality-by-Default (CbD)…

Contextuality and noncontextuality measures and generalized Bell inequalities for cyclic systems

- Physics, Mathematics
- 2020

Cyclic systems of dichotomous random variables have played a prominent role in contextuality research, describing such experimental paradigms as the Klyachko-Can-Binicoglu-Shumovky,…

Context-Content Systems of Random Variables: The Contextuality-by-Default Theory

- Mathematics, Physics
- 2015

This paper provides a systematic yet accessible presentation of the Contextuality-by-Default theory. The consideration is confined to finite systems of categorical random variables, which allows us…

Contextuality-by-Default 2.0: Systems with Binary Random Variables

- Mathematics, PhysicsQI
- 2016

The paper outlines a new development in the Contextualityby-Default theory as applied to finite systems of binary random variables, which coincides with the previous version in the important case of cyclic systems, which include the systems whose contextuality was most intensively studied in quantum physics and behavioral sciences.

The Contextuality-by-Default View of the Sheaf-Theoretic Approach to Contextuality

- Physics, Mathematics
- 2019

It is shown that when STC is applied to systems of random variables, it can be recast in the language of the Contextuality-by-Default (CbD) theory, and this allows one to extend STC to arbitrary systems, in which the requirement in question (called "consistent connectedness'" in CbD is not necessarily satisfied.

True contextuality beats direct influences in human decision making.

- Biology, PhysicsJournal of experimental psychology. General
- 2019

A series of crowd-sourcing experiments that exhibit true contextuality in simple decision making are presented, an elaboration of one introduced in the Snow Queen experiment, in which contextuality was for the first time demonstrated unequivocally.

Exploration of Contextuality in a Psychophysical Double-Detection Experiment

- Computer Science, PsychologyQI
- 2016

The Contextuality-by-Default (CbD) theory is applied to a psychophysical double-detection experiment, in which observers were asked to determine presence or absence of a signal property in each of two simultaneously presented stimuli.

Contextual Fraction as a Measure of Contextuality.

- Computer Science, PhysicsPhysical review letters
- 2017

The contextual fraction is considered as a quantitative measure of contextuality of empirical models, i.e., tables of probabilities of measurement outcomes in an experimental scenario and measures quantifiable advantages in informatic tasks, such as games and a form of measurement-based quantum computing.

Is there contextuality in behavioural and social systems?

- Computer Science, BiologyPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2016

The working hypothesis is that this may be a broadly applicable rule: behavioural and social systems are non-contextual, i.e. all ‘contextual effects’ in them result from the ubiquitous dependence of response distributions on the elements of contexts other than the ones to which the response is presumably or normatively directed.

Violation of contextual generalization of the Leggett-Garg inequality for recognition of ambiguous figures

- Mathematics, Biology
- 2014

This work derives an analog of the LG inequality, 'contextual LG inequality', and uses it as a test of 'quantum-likeness' of statistical data collected in a series of experiments on the recognition of ambiguous figures, demonstrating violation of the contextual LG inequality for some combinations of the aforementioned contexts.