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Contextuality Analysis of Impossible Figures.

Víctor H Cervantes1, Ehtibar N Dzhafarov2

  • 1Department of Psychology, University of Illinois at Urbana-Champaign, Champaign, IL 61820, USA.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary

This study analyzes contextuality in epistemic random variables using impossible figures. It evaluates a new hierarchical measure of (non)contextuality, offering insights into uncertainty and knowledge representation.

Keywords:
contextualitydeterministic systemsepistemic probabilitiesimpossible figuresmeasures of contextuality

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Area of Science:

  • Cognitive Science
  • Quantum Information Theory
  • Philosophy of Science

Background:

  • Contextuality is a key concept in quantum mechanics and cognitive science.
  • Previous measures of (non)contextuality exist but lack hierarchical structure.
  • Impossible figures provide a unique framework for analyzing deterministic and probabilistic systems.

Purpose of the Study:

  • To perform contextuality analysis on systems of epistemic random variables.
  • To evaluate the performance of a novel hierarchical measure of (non)contextuality.
  • To apply these analyses to impossible figures as deterministic and probabilistic systems.

Main Methods:

  • Developing systems of epistemic random variables by probabilistically mixing deterministic descriptions of impossible figures.
  • Applying a new hierarchical measure of (non)contextuality to these systems.
  • Analyzing the structure of uncertainty and knowledge representation within these systems.

Main Results:

  • Demonstrated the contextuality analysis of epistemic random variable systems.
  • Evaluated the performance of the hierarchical measure of (non)contextuality.
  • Showcased the utility of impossible figures in studying contextuality.

Conclusions:

  • The hierarchical measure effectively captures contextuality in epistemic systems.
  • Probabilistic mixtures of deterministic systems model uncertainty and lack of knowledge.
  • Impossible figures serve as valuable models for contextuality analysis.