7 found
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  1.  50
    On Selective Influences, Marginal Selectivity, and Bell/CHSH Inequalities.Ehtibar N. Dzhafarov & Janne V. Kujala - 2014 - Topics in Cognitive Science 6 (1):121-128.
    The Bell/CHSH inequalities of quantum physics are identical with the inequalities derived in mathematical psychology for the problem of selective influences in cases involving two binary experimental factors and two binary random variables recorded in response to them. The following points are made regarding cognitive science applications: (1) compliance of data with these inequalities is informative only if the data satisfy the requirement known as marginal selectivity; (2) both violations of marginal selectivity and violations of the Bell/CHSH inequalities are interpretable (...)
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  2.  16
    Contextuality in Three Types of Quantum-Mechanical Systems.Ehtibar N. Dzhafarov, Janne V. Kujala & Jan-Åke Larsson - 2015 - Foundations of Physics 45 (7):762-782.
    We present a formal theory of contextuality for a set of random variables grouped into different subsets corresponding to different, mutually incompatible conditions. Within each context the random variables are jointly distributed, but across different contexts they are stochastically unrelated. The theory of contextuality is based on the analysis of the extent to which some of these random variables can be viewed as preserving their identity across different contexts when one considers all possible joint distributions imposed on the entire set (...)
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  3. No-Forcing and No-Matching Theorems for Classical Probability Applied to Quantum Mechanics.Ehtibar N. Dzhafarov & Janne V. Kujala - 2014 - Foundations of Physics 44 (3):248-265.
    Correlations of spins in a system of entangled particles are inconsistent with Kolmogorov’s probability theory (KPT), provided the system is assumed to be non-contextual. In the Alice–Bob EPR paradigm, non-contextuality means that the identity of Alice’s spin (i.e., the probability space on which it is defined as a random variable) is determined only by the axis $\alpha _{i}$ chosen by Alice, irrespective of Bob’s axis $\beta _{j}$ (and vice versa). Here, we study contextual KPT models, with two properties: (1) Alice’s (...)
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  4.  9
    Proof of a Conjecture on Contextuality in Cyclic Systems with Binary Variables.Janne V. Kujala & Ehtibar N. Dzhafarov - 2016 - Foundations of Physics 46 (3):282-299.
    We present a proof for a conjecture previously formulated by Dzhafarov et al.. The conjecture specifies a measure for the degree of contextuality and a criterion for contextuality in a broad class of quantum systems. This class includes Leggett–Garg, EPR/Bell, and Klyachko–Can–Binicioglu–Shumovsky type systems as special cases. In a system of this class certain physical properties \ are measured in pairs \ \); every property enters in precisely two such pairs; and each measurement outcome is a binary random variable. Denoting (...)
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  5.  8
    Contextuality and Dichotomizations of Random Variables.Ehtibar N. Dzhafarov & Janne V. Kujala - 2021 - Foundations of Physics 52 (1):1-25.
    The Contextuality-by-Default approach to determining and measuring the contextuality of a system of random variables requires that every random variable in the system be represented by an equivalent set of dichotomous random variables. In this paper we present general principles that justify the use of dichotomizations and determine their choice. The main idea in choosing dichotomizations is that if the set of possible values of a random variable is endowed with a pre-topology, then the allowable dichotomizations split the space of (...)
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  6.  17
    Minimal Distance to Approximating Noncontextual System as a Measure of Contextuality.Janne V. Kujala - 2017 - Foundations of Physics 47 (7):911-932.
    Let random vectors \ represent joint measurements of certain subsets \ of properties\ in different contexts\. Such a system is traditionally called noncontextual if there exists a jointly distributed set \ of random variables such that \ has the same distribution as \ for all \ A trivial necessary condition for noncontextuality and a precondition for many measures of contextuality is that the system is consistently connected, i.e., all \ measuring the same property \ have the same distribution. The contextuality-by-default (...)
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  7.  20
    Beyond Quantum Probability: Another Formalism Shared by Quantum Physics and Psychology.Ehtibar N. Dzhafarov & Janne V. Kujala - 2013 - Behavioral and Brain Sciences 36 (3):283 - 284.
    There is another meeting place for quantum physics and psychology, both within and outside of cognitive modeling. In physics it is known as the issue of classical (probabilistic) determinism, and in psychology it is known as the issue of selective influences. The formalisms independently developed in the two areas for dealing with these issues turn out to be identical, opening ways for mutually beneficial interactions.
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