Quantum-like Cognition in Process Theories: An Analysis

TL;DR

This paper extends quantum-like models of cognition to general probabilistic process theories, demonstrating how many cognitive effects can be modeled diagrammatically and analyzing the limitations of classical models.

Contribution

It introduces a diagrammatic approach to process theories for modeling cognition, showing how quantum-like effects can be captured and how classical models can be challenged.

Findings

Sequential decision data can be modeled by classical instrument models.

Simple deterministic models can exhibit quantum-like cognitive effects.

Real-world data violate Bell inequalities, challenging classical models.

Abstract

Various effects in human cognition, often considered `non-classical', have been argued to be most naturally modelled by quantum-like models of decision making. We extend this approach to describe models of cognition and decision-making in general probabilistic process theories, which include both classical probabilistic models and quantum instrument models as special cases. We show how many aspects of quantum-like cognition can be described diagrammatically in process theories, before using our approach to assess the arguments for quantum-like models. While standard Bayesian classical models are insufficient, we prove that any sequential decision data can in fact be given a more general form of classical instrument model, and see that even simple deterministic models can exhibit all cognitive effects. Restricting attention to instruments induced by measurements, such as classical Bayesian and quantum POVM models, rules out such a result, but is challenged by the fact that such instruments cannot account for certain effects. Finally, we argue that to strictly rule out classical instrument models one should make use of parallel composition in the modelling of joint decisions, and find real world cognitive data violating Bell inequalities.