[1]: 752 If participants in a psychology experiment are told about "Linda", described as looking like a feminist but not like a bank teller, then asked to rank the probability,
Contextuality implies existence of incompatible mental variables, violation of the classical law of total probability, and constructive or destructive interference effects.
Suppose a person is given an opportunity to play two rounds of the following gamble: a coin toss will determine whether the subject wins $200 or loses $100.
[9][15][16] Similar violations of the sure-thing principle are seen in empirical studies of the Prisoner's Dilemma and have likewise been modeled in terms of quantum interference.
[18][19][20] These deviations can be explained if one assumes that the overall conceptual landscape influences the subject's choice in a neither predictable nor controllable way.
More explicitly, the paradoxical situations above can be represented in a unified Hilbert space formalism where human behavior under uncertainty is explained in terms of genuine quantum aspects, namely, superposition, interference, contextuality and incompatibility.
[26] The quantum model introduces a new fundamental concept to cognition—the compatibility versus incompatibility of questions and the effect this can have on the sequential order of judgments.
One can show that the true-false state of this paradox is represented in a complex Hilbert space, while the typical oscillations between true and false are dynamically described by the Schrödinger equation.
Cognitive psychology has researched different approaches for understanding concepts including exemplars, prototypes, and neural networks, and different fundamental problems have been identified, such as the experimentally tested non classical behavior for the conjunction and disjunction of concepts, more specifically the Pet-Fish problem or guppy effect,[32] and the overextension and underextension of typicality and membership weight for conjunction and disjunction.
The large amount of data collected by Hampton[33][34] on the combination of two concepts can be modeled in a specific quantum-theoretic framework in Fock space where the observed deviations from classical set (fuzzy set) theory, the above-mentioned over- and under- extension of membership weights, are explained in terms of contextual interactions, superposition, interference, entanglement and emergence.
[43][44] The research in (iv) had a deep impact on the understanding and initial development of a formalism to obtain semantic information when dealing with concepts, their combinations and variable contexts in a corpus of unstructured documents.
This conundrum of natural language processing (NLP) and information retrieval (IR) on the web – and data bases in general – can be addressed using the mathematical formalism of quantum theory.
[48] Ideas for applying the formalisms of quantum theory to cognition first appeared in the 1990s by Diederik Aerts and his collaborators Jan Broekaert, Sonja Smets and Liane Gabora, by Harald Atmanspacher, Robert Bordley, and Andrei Khrennikov.
A special issue on Quantum Cognition and Decision appeared in the Journal of Mathematical Psychology (2009, vol 53.
The first Quantum Interaction workshop was held at Stanford in 2007 organized by Peter Bruza, William Lawless, C. J. van Rijsbergen, and Don Sofge as part of the 2007 AAAI Spring Symposium Series.
This was followed by workshops at Oxford in 2008, Saarbrücken in 2009, at the 2010 AAAI Fall Symposium Series held in Washington, D.C., 2011 in Aberdeen, 2012 in Paris, and 2013 in Leicester.