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The scientific community is becoming more and more interested in the researchthat applies the mathematical formalism of quantum theory to model humandecision-making. In this paper, we provide the theoretical foundations of thequantum approach to cognition that we developed in Brussels. These foundationsrest on the results of two decade studies on the axiomatic andoperational-realistic approaches to the foundations of quantum physics. Thedeep analogies between the foundations of physics and cognition lead us toinvestigate the validity of quantum theory as a general and unitary frameworkfor cognitive processes, and the empirical success of the Hilbert space modelsderived by such investigation provides a strong theoretical confirmation ofthis validity. However, two situations in the cognitive realm, 'question ordereffects' and 'response replicability', indicate that even the Hilbert spaceframework could be insufficient to reproduce the collected data. This does notmean that the mentioned operational-realistic approach would be incorrect, butsimply that a larger class of measurements would be in force in humancognition, so that an extended quantum formalism may be needed to deal with allof them. As we will explain, the recently derived 'extended Blochrepresentation' of quantum theory (and the associated 'generaltension-reduction' model) precisely provides such extended formalism, whileremaining within the same unitary interpretative framework.

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