Noncontextuality with Marginal Selectivity in Reconstructing Mental Architectures

TL;DR

This paper develops a general theoretical framework for analyzing series-parallel mental architectures with selectively influenced, non-independent components, using concepts from quantum contextuality to understand how processes are arranged.

Contribution

It introduces a novel, more general method for analyzing the interaction contrasts in mental architectures based on noncontextuality and marginal selectivity principles.

Findings

Provides a mathematical approach to test for noncontextuality in mental processes.

Extends previous methods to more complex series-parallel architectures.

Offers a new perspective linking quantum theory concepts to cognitive architecture analysis.

Abstract

We present a general theory of series-parallel mental architectures with selectively influenced stochastically non-independent components. A mental architecture is a hypothetical network of processes aimed at performing a task, of which we only observe the overall time it takes under variable parameters of the task. It is usually assumed that the network contains several processes selectively influenced by different experimental factors, and then the question is asked as to how these processes are arranged within the network, e.g., whether they are concurrent or sequential. One way of doing this is to consider the distribution functions for the overall processing time and compute certain linear combinations thereof (interaction contrasts). The theory of selective influences in psychology can be viewed as a special application of the interdisciplinary theory of (non)contextuality having its origins and main applications in quantum theory. In particular, lack of contextuality is equivalent to the existence of a "hidden" random entity of which all the random variables in play are functions. Consequently, for any given value of this common random entity, the processing times and their compositions (minima, maxima, or sums) become deterministic quantities. These quantities, in turn, can be treated as random variables with (shifted) Heaviside distribution functions, for which one can easily compute various linear combinations across different treatments, including interaction contrasts. This mathematical fact leads to a simple method, more general than the previously used ones, to investigate and characterize the interaction contrast for different types of series-parallel architectures.