On contextuality in behavioural data

Dzhafarov, Ehtibar N.; Kujala, Janne V.; Cervantes, Víctor H.; Zhang, Ru; Jones, Matt

doi:10.1098/rsta.2015.0234

Cited by 39 publications

(73 citation statements)

References 35 publications

(162 reference statements)

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“…The Contextualityby-Default (CbD) theory [16, 18, 20-25, 27, 28, 30] overcomes this difficulty by proposing a principled way of separating contextuality proper from inconsistent connectedness (the CbD term for violations of the "no-signaling" or "marginal selectivity" condition). This theory was used to reanalyze the behavioral experiments aimed at contextuality, with the conclusion that they provide no evidence for contextuality [14,29,31,53]: inconsistent connectedness is the only form of context-dependence that we have in them. By contrast, when CbD is used to reanalyze a quantum-mechanical experiment that exhibits inconsistent connectedness [42], contextuality proper (on top of inconsistent connectedness) is established beyond doubt [39].…”

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confidence: 99%

Advanced analysis of quantum contextuality in a psychophysical double-detection experiment

Cervantes

Dzhafarov

2017

Journal of Mathematical Psychology

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The results of behavioral experiments typically exhibit inconsistent connectedness, i.e., they violate the condition known as "no-signaling," "no-disturbance," or "marginal selectivity." This prevents one from evaluating these experiments in terms of quantum contextuality if the latter understood traditionally (as, e.g., in the Kochen-Specker theorem or Bell-type inequalities). The Contextualityby-Default (CbD) theory separates contextuality from inconsistent connectedness. When applied to quantum physical experiments that exhibit inconsistent connectedness (due to context-dependent errors and/or signaling), the CbD computations reveal quantum contextuality in spite of this. When applied to a large body of published behavioral experiments, the CbD computations reveal no quantum contextuality: all context-dependence in these experiments is described by inconsistent connectedness alone. Until recently, however, experimental analysis of contextuality was confined to so-called cyclic systems of binary random variables. Here, we present the results of a psychophysical double-detection experiment that do not form a cyclic system: their analysis requires that we use a recent modification of CbD, one that makes the class of noncontextual systems more restricted. Nevertheless our results once again indicate that when inconsistent connectedness is taken into account, the system exhibits no contextuality.KEYWORDS: contextuality, cyclic systems, double-detection, inconsistent connectedness, psychophysics.In recent years there were many reports of behavioral experiments [1, 4-7, 11, 14, 31, 34, 47, 51, 53] aimed at (or interpretable as aimed at) revealing contextuality of the kind predicted by and experimentally confirmed in quantum physics [10,15,32,33,35,36,41,42]. All known to us behavioral data, however, violate a certain condition that makes a direct application of the traditional quantum contextuality analysis impossible. This condition is variously called "no-signaling" or "no-disturbance" in quantum physics [8,9,13,37,40,45,46] and "marginal selectivity" in psychology [17,50,52]. It is a required condition for the traditional quantum contextuality analysis, even though it is often violated in quantum mechanical experiments as well (this issue was first systematically discussed in [2]; see also ([3, 42, 43]). The Contextualityby-Default (CbD) theory [16, 18, 20-25, 27, 28, 30] overcomes this difficulty by proposing a principled way of separating contextuality proper from inconsistent connectedness (the CbD term for violations of the "no-signaling" or "marginal selectivity" condition). This theory was used to reanalyze the behavioral experiments aimed at contextuality, with the conclusion that they provide no evidence for contextuality [14,29,31,53]: inconsistent connectedness is the only form of context-dependence that we have in them. By contrast, when CbD is used to reanalyze a quantum-mechanical experiment that exhibits inconsistent connectedness [42], contextuality proper (on top of inconsistent connectedness) i...

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confidence: 99%

Advanced analysis of quantum contextuality in a psychophysical double-detection experiment

Cervantes

Dzhafarov

2017

Journal of Mathematical Psychology

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“…This is the starting point of a variant (or implementation) of KPT that we dubbed Contextuality‐by‐Default (CbD) . Applying it to the KCBS example, the matrix should be filled in as

([], \begin{matrix} (K C B S) & c_{1} & c_{2} & c_{3} & c_{4} & c_{5} \\ q_{1} & R_{1}^{1} & R_{1}^{5} \\ q_{2} & R_{2}^{1} & R_{2}^{2} \\ q_{3} & R_{3}^{2} & R_{3}^{3} \\ q_{4} & R_{4}^{3} & R_{4}^{4} \\ q_{5} & R_{5}^{4} & R_{5}^{5} \end{matrix})

Here,

R_{q_{i}}^{c_{j}}

(written as

R_{i}^{j}

for simplicity) is a unique (within the given system) identification of the random random variable as measuring

q_{i}

in context

c_{j}

.…”

Section: What Is Contextuality?mentioning

confidence: 99%

“…One can consider all possible distributions satisfying and find out that the system is noncontextual if and only if

|(〈〉, R_{a}^{a b}) - (〈〉, R_{a}^{c a})| + |(〈〉, R_{b}^{a b}) - (〈〉, R_{b}^{b c})| + |(〈〉, R_{c}^{b c}) - (〈〉, R_{c}^{c a})| \geq 2 .

In particular, the system is noncontextual if for at least one pair of boxes the gem always appears in a particular one of them. If this is true for all three pairs of boxes, the system is deterministic, and any deterministic system is noncontextual . And so on, one can proceed investigating this magic system from a variety of angles.…”

Section: Summarizing With Magic Boxesmentioning

confidence: 99%

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Probabilistic foundations of contextuality

Dzhafarov

Kujala

2016

Fortschritte der Physik

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Contextuality is usually defined as absence of a joint distribution for a set of measurements (random variables) with known joint distributions of some of its subsets. However, if these subsets of measurements are not disjoint, contextuality is mathematically impossible even if one generally allows (as one must) for random variables not to be jointly distributed. To avoid contradictions one has to adopt the Contextuality‐by‐Default approach: measurements made in different contexts are always distinct and stochastically unrelated to each other. Contextuality is reformulated then in terms of the (im)possibility of imposing on all the measurements in a system a joint distribution of a particular kind: such that any measurements of one and the same property made in different contexts satisfy a specified property, scriptC. In the traditional analysis of contextuality scriptC means “are equal to each other with probability 1”. However, if the system of measurements violates the “no‐disturbance principle”, due to signaling or experimental biases, then the meaning of scriptC has to be generalized, and the proposed generalization is “are equal to each other with maximal possible probability” (applied to any set of measurements of one and the same property). This approach is illustrated on arbitrary systems of binary measurements, including most of quantum systems of traditional interest in contextuality studies (irrespective of whether the “no‐disturbance” principle holds in them).

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“…Andrei Khrennikov [28] announced QBism as the most natural interpretation of quantum cognition, as representing the private agent perspective in the process of decision making based on assignment of subjective probabilities. Inter-relation of quantum foundations and psychology was also enlighten in the paper of Ehtibar Dzhafarov et al [29]. Another contribution devoted to application of methods of quantum mechanics outside of physics is the article of Emmanuel Haven [30].…”

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confidence: 99%

Preface of the special issue quantum foundations: information approach

D’Ariano

Khrennikov

2016

Phil. Trans. R. Soc. A.

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One contribution of 14 to a theme issue 'Quantum foundations: information approach' . This special issue is based on the contributions of a group of top experts in quantum foundations and quantum information and probability. It enlightens a number of interpretational, mathematical and experimental problems of quantum theory.The quantum information revolution has renewed the interest in the foundations of quantum theory, upon regarding the theory from the novel informationtheoretical perspective [1][2][3][4][5]. 'Information' is the new paradigm reflecting the main character of modern human society as an information society. The tremendous development of information technologies of the last 20 years has dramatically changed our lifestyle through the world-wide web of the Internet and the mobileconnectivity web that have led to the creation of virtual social networks. The new quantum information technologies (quantum cryptography, quantum computing, quantum simulators and networks) have added a new relevant step forward for the information evolution of the mankind.Unavoidably, the new information culture has deeply influenced the thinking of scientists, and has become a new paradigm in research in quantum foundations. On the experimental side, the new quantum technology has led to closing the quantum efficiency loophole in Bell inequality tests [6,7], thus Bell's hypothesis [8] that the quantum formalism is compatible with a hiddenvariable realist interpretation can now be rejected on an experimental basis.Of course, a non-local or contextual realism is still compatible with quantum theory, as in the case of David Bohm's mechanics, which, however, still fails in reproducing a relativistic covariant theory and in

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On contextuality in behavioural data

Cited by 39 publications

References 35 publications

Advanced analysis of quantum contextuality in a psychophysical double-detection experiment

Advanced analysis of quantum contextuality in a psychophysical double-detection experiment

Probabilistic foundations of contextuality

Preface of the special issue quantum foundations: information approach

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