Abstract
The mathematical formalism of quantum theory exhibits significant effectiveness when applied to cognitive phenomena that have resisted traditional (set theoretical) modeling. Relying on a decade of research on the operational foundations of micro-physical and conceptual entities, we present a theoretical framework for the representation of concepts and their conjunctions and disjunctions that uses the quantum formalism. This framework provides a unified solution to the ‘conceptual combinations problem’ of cognitive psychology, explaining the observed deviations from classical (Boolean, fuzzy set and Kolmogorovian) structures in terms of genuine quantum effects. In particular, natural concepts ‘interfere’ when they combine to form more complex conceptual entities, and they also exhibit a ‘quantum-type context-dependence’, which are responsible of the ‘over- and under-extension’ that are systematically observed in experiments on membership judgments.
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Notes
- 1.
In this paper, we refer to set theoretical structures as ‘classical structures’, because they were originally used to represent systems and interactions in classical physics, and later were extended to psychology, economics, statistics, finance, etc. Analogously, we refer to deviations from set theoretical modeling as ‘deviations from classicality’.
- 2.
Interestingly, the approach allowed to put into evidence an important shortcoming of the standard quantum formalism: the impossibility of describing experimentally separated entities [19].
- 3.
A difference between psychological and physics laboratories is that in the former each participant works as a distinct measuring apparatus, usually producing a single outcome, whereas in the latter a same apparatus is usually used to produce multiple outcomes; see the discussion in [25].
- 4.
For instance, more general rules of probabilistic assignment than the Born one seem to be necessary for a complete modeling of question order effects data [25].
- 5.
This is similar to the prototypical example of the two-slit experiment, where a genuine interference pattern emerges when both slits are open, which cannot be explained in a compositional way, i.e., by assuming that the quantum entities (for example, photons) always pass through one or the other slit.
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Aerts, D. et al. (2017). Context and Interference Effects in the Combinations of Natural Concepts. In: Brézillon, P., Turner, R., Penco, C. (eds) Modeling and Using Context. CONTEXT 2017. Lecture Notes in Computer Science(), vol 10257. Springer, Cham. https://doi.org/10.1007/978-3-319-57837-8_54
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