The rational status of quantum cognition

Area of Science:

• Cognitive Science
• Probability Theory
• Quantum Mechanics

Background:

• Classical probability theory (CPT) is the standard for rational inference, but empirical findings like the conjunction fallacy (CF) suggest human irrationality.
• Quantum probability theory (QPT) offers an alternative framework where CFs may be consistent with rational decision-making.

Purpose of the Study:

• To evaluate the rational status of QPT using the Dutch Book (DB) argument, typically applied to CPT.
• To empirically investigate whether the conjunction fallacy (CF) can be considered rational under specific conditions.
• To explore the real-world applicability of rational CF conditions.

Main Methods:

• Proving QPT's rationality by extending CPT to include context-dependent probability spaces.
• Conducting empirical studies to assess participant rationality relative to their chosen representations.
• Analyzing the conditions under which CFs are rational and their external validity.

Main Results:

• QPT is demonstrated to be rational, interpretable as a special case of extended CPT with contextuality.
• Empirical findings indicate participants reason rationally within their employed representational frameworks.
• The conditions for rational CFs are explored for both mental and external contexts.

Conclusions:

• QPT provides a valid alternative to CPT for rational probabilistic inference, especially when contextuality is considered.
• Human reasoning, particularly concerning the CF, can be rational when viewed through the lens of QPT or context-dependent CPT.
• Contextuality is a key factor in understanding rational inference, necessitating either separate CPT spaces or QPT principles.