# Contextuality as an extension of selective influences

In 1969 Sternberg introduced the notion of experimental factors selectively influencing random variables representing mental processes. In the early 2000s this notion was extended to stochastically non-independent variables. Traditionally one uses it by postulating a pattern of selective influences, and reconstructing "mental architectures" from the overall effect of the experimental factors on some overall measure of performance, e.g., response time. However, whenever one relates experimental factors to random variables that are directly observable, one finds that the pattern of influences is not selective: it invariably violates marginal selectivity, the crudest necessary condition of selectiveness. This prevents one from applying selective influences to such seemingly closely related issues as separability/integrality of perceptual tasks. In fact, the notion of selective influences seems to have no applications except to hypothetical variables one cannot observe — an intellectually unsatisfactory situation. The modern contextuality analysis, in which theory of selective influences converges with foundations of quantum mechanics, provides a way out, and offers a powerful mathematical language for addressing in a new way a variety of traditional issues, including the separability/integrality one. The notion of selective influences is a special case of a noncontextual system with marginal selectivity. However, in the theory dubbed Contextuality-by-Default, a system can be noncontextual or contextual irrespective of whether marginal selectivity is satisfied, and the degree of both contextuality and noncontextuality can be measured together with the degree of marginal selectivity. The theory also has prominent applications outside psychology, e.g., in quantum physics and computer science.

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Hello Ehtibar: As usual, incisive logical clarity, depth, and novelty. I'll look forward to digging into your new analyses in more detail and trying to relate them to my own less formal discussion of the relationships of selective influence (SI) to perceptual separability (PS) in the recent systems factorial technology book. In addition to the in...

I have two questions: 1. The general definition of noncontextuality allows for a violation of marginal selectivity, as long as it holds "with maximal possible probability". Does this mean that the violations are only apparent violations and it is still assumed that the probability distributions show marginal selectivity (i.e., it is a stochastic...

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