On the Foundations of the Brussels Operational-Realistic Approach to Cognition

TL;DR

This paper develops a foundational quantum approach to cognition based on operational-realistic principles, extending traditional Hilbert space models with an advanced formalism to account for complex cognitive phenomena.

Contribution

It introduces an extended quantum formalism, the extended Bloch representation, to better model cognitive processes like question order effects and response replicability.

Findings

Empirical success of Hilbert space models supports quantum cognition validity.

Extended formalism addresses limitations of standard quantum models in cognition.

The framework remains within a unitary interpretative approach.

Abstract

The scientific community is becoming more and more interested in the research that applies the mathematical formalism of quantum theory to model human decision-making. In this paper, we provide the theoretical foundations of the quantum approach to cognition that we developed in Brussels. These foundations rest on the results of two decade studies on the axiomatic and operational-realistic approaches to the foundations of quantum physics. The deep analogies between the foundations of physics and cognition lead us to investigate the validity of quantum theory as a general and unitary framework for cognitive processes, and the empirical success of the Hilbert space models derived by such investigation provides a strong theoretical confirmation of this validity. However, two situations in the cognitive realm, 'question order effects' and 'response replicability', indicate that even the Hilbert space framework could be insufficient to reproduce the collected data. This does not mean that the mentioned operational-realistic approach would be incorrect, but simply that a larger class of measurements would be in force in human cognition, so that an extended quantum formalism may be needed to deal with all of them. As we will explain, the recently derived 'extended Bloch representation' of quantum theory (and the associated 'general tension-reduction' model) precisely provides such extended formalism, while remaining within the same unitary interpretative framework.