Contextuality Analysis of Impossible Figures.

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.