0000000001043895
AUTHOR
Víctor H. Cervantes
On Contextuality in Behavioral Data
Dzhafarov, Zhang, and Kujala (Phil. Trans. Roy. Soc. A 374, 20150099) reviewed several behavioral data sets imitating the formal design of the quantum-mechanical contextuality experiments. The conclusion was that none of these data sets exhibited contextuality if understood in the generalized sense proposed in Dzhafarov, Kujala, and Larsson (Found. Phys. 7, 762-782, 2015), while the traditional definition of contextuality does not apply to these data because they violate the condition of consistent connectedness (also known as marginal selectivity, no-signaling condition, no-disturbance principle, etc.). In this paper we clarify the relationship between (in)consistent connectedness and (non…
Contextuality in canonical systems of random variables
Random variables representing measurements, broadly understood to include any responses to any inputs, form a system in which each of them is uniquely identified by its content (that which it measures) and its context (the conditions under which it is recorded). Two random variables are jointly distributed if and only if they share a context. In a canonical representation of a system, all random variables are binary, and every content-sharing pair of random variables has a unique maximal coupling (the joint distribution imposed on them so that they coincide with maximal possible probability). The system is contextual if these maximal couplings are incompatible with the joint distributions o…
Contextuality-by-Default: A Brief Overview of Ideas, Concepts, and Terminology
This paper is a brief overview of the concepts involved in measuring the degree of contextuality and detecting contextuality in systems of binary measurements of a finite number of objects. We discuss and clarify the main concepts and terminology of the theory called “contextuality-by-default,” and then discuss generalizations of the theory to arbitrary systems of arbitrary random variables.
A Supplementary Text to “Contextuality in Canonical Systems of Random Variables” by Ehtibar N. Dzhafarov, Víctor H. Cervantes, and Janne V. Kujala (Phil. Trans. Roy. Soc. A xxx, 10.1098/rsta.xxxx.xxxx) from Contextuality in canonical systems of random variables
Mathematical Proofs