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Quantum Structure in Cognition and the Foundations of Human Reasoning

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Abstract

Traditional cognitive science rests on a foundation of classical logic and probability theory. This foundation has been seriously challenged by several findings in experimental psychology on human decision making. Meanwhile, the formalism of quantum theory has provided an efficient resource for modeling these classically problematical situations. In this paper, we start from our successful quantum-theoretic approach to the modeling of concept combinations to formulate a unifying explanatory hypothesis. In it, human reasoning is the superposition of two processes – a conceptual reasoning, whose nature is emergence of new conceptuality, and a logical reasoning, founded on an algebraic calculus of the logical type. In most cognitive processes however, the former reasoning prevails over the latter. In this perspective, the observed deviations from classical logical reasoning should not be interpreted as biases but, rather, as natural expressions of emergence in its deepest form.

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Notes

  1. Our use of Fock space agrees with its mathematical definition as an infinite direct sum of Hilbert spaces. However, we limit ourselves to consider only two sectors here, because we are interested in the combination of two concepts. The generalization to the combination of a larger (and even infinite) number of concepts is straightforward, as shown in [11]. In any case, to avoid confusion, we will refer to “two-sector Fock space” in this paper. It is interesting to notice that our definition of Fock space does not include superselection rules (i.e. no symmetries with respect to particles exhange are needed), as in the case of the Fock space used in particle physics.

  2. The projection operator M represents the decision measurement of a subject who estimates the membership of an item, say x, to a concept, say A. Hence, the membership weight can be expressed, by using Born rule, as μ(A)=〈A|M|A〉. By following standard quantum rules, one could then be led to think that the vector M|A〉 represents, up to a normalization factor, some kind of final state after a decision measurement. However, such an interpretation would presuppose that these decision measurements can be considered as ideal measurements of the first kind, in the standard quantum sense, which is quite controversial in quantum cognition. In any case, our approach does not need any final state after the measurement, or wave function collapse, as it only relies on Born rule for probabilities.

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Aerts, D., Sozzo, S. & Veloz, T. Quantum Structure in Cognition and the Foundations of Human Reasoning. Int J Theor Phys 54, 4557–4569 (2015). https://doi.org/10.1007/s10773-015-2717-9

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