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.
Highlights
A fundamental problem in cognition concerns the identification of the principles guiding human decision-making
Increasing experimental evidence on conceptual categorization, probability judgments, and behavioral economics confirms that this classical conception is fundamentally problematical, in the sense that the cognitive models based on these mathematical structures are not capable of capturing how people concretely take decisions in situations of uncertainty
We followed an axiomatic and operational-realistic approach to quantum physics, in which we investigated how the mathematical formalism of quantum theory in Hilbert space can be derived from more intuitive and physically justified axioms, directly connected with empirical situations and facts
Summary
A fundamental problem in cognition concerns the identification of the principles guiding human decision-making. We followed an axiomatic and operational-realistic approach to quantum physics, in which we investigated how the mathematical formalism of quantum theory in Hilbert space can be derived from more intuitive and physically justified axioms, directly connected with empirical situations and facts. This led us to elaborate a “State Context Property” (SCoP) formalism, according to which any physical entity is expressed in terms of the operationally well defined notions of “state,” “context,” and “property,” and functional relations between these notions [29]. We believe that new mathematical structures, more general than both pure classical and pure quantum structures, will be needed in the modeling of cognitive processes
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