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Concepts and their dynamics: A quantumtheoretic modeling of human thought
 Topics in Cognitive Science
, 2013
"... We analyze different aspects of our quantum modeling approach of human concepts, and more specifically focus on the quantum effects of contextuality, interference, entanglement and emergence, illustrating how each of them makes its appearance in specific situations of the dynamics of human concepts ..."
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We analyze different aspects of our quantum modeling approach of human concepts, and more specifically focus on the quantum effects of contextuality, interference, entanglement and emergence, illustrating how each of them makes its appearance in specific situations of the dynamics of human concepts and their combinations. We point out the relation of our approach, which is based on an ontology of a concept as an entity in a state changing under influence of a context, with the main traditional concept theories, i.e. prototype theory, exemplar theory and theory theory. We ponder about the question why quantum theory performs so well in its modeling of human concepts, and shed light on this question by analyzing the role of complex amplitudes, showing how they allow to describe interference in the statistics of measurement outcomes, while in the traditional theories statistics of outcomes originates in classical probability weights, without the possibility of interference. The relevance of complex numbers, the appearance of entanglement, and the role of Fock space in explaining contextual emergence, all as unique features of the quantum modeling, are explicitly revealed in this paper by analyzing human concepts and their dynamics.
Concepts and Bounded Rationality: An Application of Niestegge’s Approach to Conditional Quantum Probabilities
"... Abstract. Recently, Gerd Niestegge developed a new approach to quantum mechanics via conditional probabilities developing the wellknown proposal to consider the Lüdersvon Neumann measurement as a nonclassical extension of probability conditionalization. I will apply his powerful and rigorous appr ..."
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Abstract. Recently, Gerd Niestegge developed a new approach to quantum mechanics via conditional probabilities developing the wellknown proposal to consider the Lüdersvon Neumann measurement as a nonclassical extension of probability conditionalization. I will apply his powerful and rigorous approach to the treatment of concepts using a geometrical model of meaning. In this model, instances are treated as vectors of a Hilbert space ℋ. In the present approach there are at least two possibilities to form categories. The first possibility sees categories as a mixture of its instances (described by a density matrix). In the simplest case we get the classical probability theory including the Bayesian formula. The second possibility sees categories formed by a distinctive prototype which is the superposition of the (weighted) instances. The construction of prototypes can be seen as transferring a mixed quantum state into a pure quantum state freezing the probabilistic characteristics of the superposed instances into the structure of the formed prototype. Closely related to the idea of forming concepts by prototypes is the existence of interference effects. Such inference effects are typically found in macroscopic quantum systems and I will discuss them in connection with several puzzles of bounded rationality. The present approach nicely generalizes earlier proposals made by authors such as Diederik Aerts, Andrei Khrennikov, Ricardo Franco, and Jerome Busemeyer. Concluding, I will suggest that an active dialogue between cognitive approaches to logic and semantics and the modern approach of quantum information science is mandatory.
A quantum probability explanation in Fock space for borderline contradictions
 Journal of Mathematical Psychology
, 2014
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A quantum cognition analysis of the Ellsberg paradox
 in Proceedings of QI 2011Fifth International Symposium on Quantum Interaction, edited by D. Song, M. Melucci, and I. Frommholz, LNCS 7052
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Two Qubits for C.G. Jung's Theory of Personality
"... We propose a formalization of C.G. Jung's theory of personality using a fourdimensional Hilbertspace for the representation of two qubits. The first qubit relates to Jung's four psychological functions Thinking, Feeling, Sensing and iNtuition, which are represented by two groups of proje ..."
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We propose a formalization of C.G. Jung's theory of personality using a fourdimensional Hilbertspace for the representation of two qubits. The first qubit relates to Jung's four psychological functions Thinking, Feeling, Sensing and iNtuition, which are represented by two groups of projection operators {T, F} and {S, N}. The operators in each group are commuting but operators of different groups are not. The second qubit represents Jung's two perspectives of extraversion and introversion. It is shown that this system gives a natural explanation of the 16 psychological types that are defined in the Jungian tradition. Further, the system accounts for the restriction posed by Jung concerning the possible combination of psychological functions and perspectives. Interestingly, the unitary transformation called Xgate in the quantum computation community realizes the cognitive operation connected to Jung's idea of the shadow. The empirical consequences of the present model are discussed and it is shown why the present praxis of personality diagnostics based on classical statistics is insufficient. 1
TIgames I: An Exploration of Type Indeterminacy in Strategic Decisionmaking
, 2009
"... The Type Indeterminacy model is a theoretical framework that formalizes the constructive preference perspective suggested by Kahneman and Tversky. In this paper we explore an extention of the TImodel from simple to strategic decisionmaking. A 2X2 game is investigated. We first show that in a ones ..."
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The Type Indeterminacy model is a theoretical framework that formalizes the constructive preference perspective suggested by Kahneman and Tversky. In this paper we explore an extention of the TImodel from simple to strategic decisionmaking. A 2X2 game is investigated. We first show that in a oneshot simultaneaous move setting the TImodel is equivalent to a standard incomplete information model. We then let the game be preceded by a cheaptalk promise exchange game. We show in an example that in the TImodel the promise stage can have impact on next following behavior when the standard classical model predicts no impact whatsoever. The TI approach differs from other behavioral approaches in identifying the source of the effect of cheaptalk promises in the intrinsic indeterminacy of the players ’ type.
The Potential of Quantum Probability for Modeling Cognitive Processes
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On a General Bayesian Pattern Logic of FrequencyBased Logical Inclusion Fallacies
 In Proceedings of the ThirtyFirst Annual Conference of the Cognitive Science Society. Austin, TX: Cognitive Science Society
, 2009
"... Bayesian logic provides a rational model of probability judgments deviating from the standard extensional norm of extensional probability. It formalizes the general idea of an inductive pattern logic that may resolve paradoxes of inclusion. Bayesian logic predicts that it should be possible to gener ..."
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Bayesian logic provides a rational model of probability judgments deviating from the standard extensional norm of extensional probability. It formalizes the general idea of an inductive pattern logic that may resolve paradoxes of inclusion. Bayesian logic predicts that it should be possible to generalize the phenomenon of frequencybased logical conjunction fallacies to a system of logical inclusion fallacies. In Experiment 1 quantitative conditions for conjunction fallacies and the role of negations are investigated. Experiment 2 provides a first test of the postulated more general system of logical inclusion fallacies. The results of both experiments confirmed the proposed pattern logic and its formalization as Bayesian logic. Other theories of the conjunction fallacy cannot readily explain this class of frequencybased and patternbased inclusion fallacies. Whether there are simpler heuristics that may perhaps explain these data as well should be investigated in the future.