Quantum structure in cognition

Abstract

The broader scope of our investigations is the search for the way in which concepts and their combinations carry and influence meaning and what this implies for human thought. More specifically, we examine the use of the mathematical formalism of quantum mechanics as a modeling instrument and propose a general mathematical modeling scheme for the combinations of concepts. We point out that quantum mechanical principles, such as superposition and interference, are at the origin of specific effects in cognition related to concept combinations, such as the guppy effect and the overextension and underextension of membership weights of items. We work out a concrete quantum mechanical model for a large set of experimental data of membership weights with overextension and underextension of items with respect to the conjunction and disjunction of pairs of concepts, and show that no classical model is possible for these data. We put forward an explanation by linking the presence of quantum aspects that model concept combinations to the basic process of concept formation. We investigate the implications of our quantum modeling scheme for the structure of human thought, and show the presence of a two-layer structure consisting of a classical logical layer and a quantum conceptual layer. We consider connections between our findings and phenomena such as the disjunction effect and the conjunction fallacy in decision theory, violations of the sure thing principle, and the Allais and Elsberg paradoxes in economics.

A quantum geometric model of similarity.

“…A superposition state vector cannot be said to possess a specific value for any of these possible outcomes and possible outcomes may interfere with each other, as the state vector develops in time. These features of quantum theory have enabled probabilistic models for situations which have been puzzling from a classical perspective (Aerts, 2009;Atmanspacher et al, 2004;Blutner, 2008;Bruza, 2010;Busemeyer & Bruza, 2012;Khrennikov, 2004;Yukalov & Sornette, 2010). A general difference between quantum and classical theories is that the latter require that there is always a complete joint probability distribution for all the questions relevant for a system (this is the principle of unicity; Griffiths, 2003).…”

Sometimes it does hurt to ask: The constructive role of articulating impressions

“…Other QP approaches to decision making are based on the same core principles of QP theory and, specifically, share the key assumption employed presently, that a decision must involve a corresponding projection of the state vector (e.g., Aerts, 2009;Asano et al, 2011a, Asano et al, 2012Pothos & Busemeyer, 2009;Yukalov & Sornette, 2010). 3 Note that different QP models do somewhat differ in the psychological assumptions which they embody, over and above core quantum principles.…”

“…For example, since Wason's (1960) results showing that naïve observers do not appear to reason in a way consistent with classical logic (cf. Anderson, 1991;Feldman, 2000), CP theory has been the major route through which researchers have sought to reformulate our understanding of human rationality (Oaksford & Chater, 2007, 2009). Could we employ CP theory to model the constructive role of certain judgments?…”

Quantization and Quantum-Like Phenomena: A Number Amplitude Approach

“…However, it is possible to infer certain properties from Eqs. (21) and (22). Let us de…ne as a unit vector in a complex Hilbert space that is an eigenvector of K , with an eigenvalue of , i.e.…”

“…This then leaves us free to interpret our results in a way less constrained by our foundational assumptions. This is important since considerable interest has arisen, over the past decade or so, in the application of quantum formalism to non-physical systems, ranging, for example, from …nance [18], [19] and population dynamics [20] to social science [21], psychology [22], cognition [23] and neuroscience [24]. Khrennikov [25] has coined the phrase quantum-like to describe such processes.…”