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  1. Conditions for Quantum Interference in Cognitive Sciences.Vyacheslav I. Yukalov & Didier Sornette - 2014 - Topics in Cognitive Science 6 (1):79-90.
    We present a general classification of the conditions under which cognitive science, concerned, e.g. with decision making, requires the use of quantum theoretical notions. The analysis is done in the frame of the mathematical approach based on the theory of quantum measurements. We stress that quantum effects in cognition can arise only when decisions are made under uncertainty. Conditions for the appearance of quantum interference in cognitive sciences and the conditions when interference cannot arise are formulated.
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  • The Potential of Using Quantum Theory to Build Models of Cognition.Zheng Wang, Jerome R. Busemeyer, Harald Atmanspacher & Emmanuel M. Pothos - 2013 - Topics in Cognitive Science 5 (4):672-688.
    Quantum cognition research applies abstract, mathematical principles of quantum theory to inquiries in cognitive science. It differs fundamentally from alternative speculations about quantum brain processes. This topic presents new developments within this research program. In the introduction to this topic, we try to answer three questions: Why apply quantum concepts to human cognition? How is quantum cognitive modeling different from traditional cognitive modeling? What cognitive processes have been modeled using a quantum account? In addition, a brief introduction to quantum probability (...)
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  • A Quantum Question Order Model Supported by Empirical Tests of an A Priori and Precise Prediction.Zheng Wang & Jerome R. Busemeyer - 2013 - Topics in Cognitive Science 5 (4):689-710.
    Question order effects are commonly observed in self-report measures of judgment and attitude. This article develops a quantum question order model (the QQ model) to account for four types of question order effects observed in literature. First, the postulates of the QQ model are presented. Second, an a priori, parameter-free, and precise prediction, called the QQ equality, is derived from these mathematical principles, and six empirical data sets are used to test the prediction. Third, a new index is derived from (...)
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  • Quantum Teleportation and Grover’s Algorithm Without the Wavefunction.Gerd Niestegge - 2017 - Foundations of Physics 47 (2):274-293.
    In the same way as the quantum no-cloning theorem and quantum key distribution in two preceding papers, entanglement-assisted quantum teleportation and Grover’s search algorithm are generalized by transferring them to an abstract setting, including usual quantum mechanics as a special case. This again shows that a much more general and abstract access to these quantum mechanical features is possible than commonly thought. A non-classical extension of conditional probability and, particularly, a very special type of state-independent conditional probability are used instead (...)
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  • A Representation of Quantum Measurement in Nonassociative Algebras.Gerd Niestegge - 2009 - Foundations of Physics 39 (2):120-136.
    Starting from an abstract setting for the Lüders-von Neumann quantum measurement process and its interpretation as a probability conditionalization rule in a non-Boolean event structure, the author derived a certain generalization of operator algebras in a preceding paper. This is an order-unit space with some specific properties. It becomes a Jordan operator algebra under a certain set of additional conditions, but does not own a multiplication operation in the most general case. A major objective of the present paper is the (...)
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  • A Representation of Quantum Measurement in Order-Unit Spaces.Gerd Niestegge - 2008 - Foundations of Physics 38 (9):783-795.
    A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach is based on the concept of conditional probability and the interpretation of the Lüders-von Neumann quantum measurement as a probability conditionalization rule. A major result shows that the operator algebras must be replaced by order-unit spaces with some specific properties in the generalized approach, and it is analyzed under which conditions these order-unit spaces become Jordan algebras. An application of this result provides a (...)
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  • Order Effects in Dynamic Semantics.Peter Beim Graben - 2014 - Topics in Cognitive Science 6 (1):67-73.
    In their target article, Wang and Busemeyer (2013) discuss question order effects in terms of incompatible projectors on a Hilbert space. In a similar vein, Blutner recently presented an orthoalgebraic query language essentially relying on dynamic update semantics. Here, I shall comment on some interesting analogies between the different variants of dynamic semantics and generalized quantum theory to illustrate other kinds of order effects in human cognition, such as belief revision, the resolution of anaphors, and default reasoning that result from (...)
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  • Questions and Answers in an Orthoalgebraic Approach.Reinhard Blutner - 2012 - Journal of Logic, Language and Information 21 (3):237-277.
    Taking the lead from orthodox quantum theory, I will introduce a handy generalization of the Boolean approach to propositions and questions: the orthoalgebraic framework. I will demonstrate that this formalism relates to a formal theory of questions (or ‘observables’ in the physicist’s jargon). This theory allows formulating attitude questions, which normally are non-commuting, i.e., the ordering of the questions affects the answer behavior of attitude questions. Further, it allows the expression of conditional questions such as “If Mary reads the book, (...)
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  • Quantum cognition and bounded rationality.Reinhard Blutner & Peter Beim Graben - 2016 - Synthese 193 (10).
    We consider several puzzles of bounded rationality. These include the Allais- and Ellsberg paradox, the disjunction effect, and related puzzles. We argue that the present account of quantum cognition—taking quantum probabilities rather than classical probabilities—can give a more systematic description of these puzzles than the alternate treatments in the traditional frameworks of bounded rationality. Unfortunately, the quantum probabilistic treatment does not always provide a deeper understanding and a true explanation of these puzzles. One reason is that quantum approaches introduce additional (...)
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  • A Quantum Probability Perspective on Borderline Vagueness.Reinhard Blutner, Emmanuel M. Pothos & Peter Bruza - 2013 - Topics in Cognitive Science 5 (4):711-736.
    The term “vagueness” describes a property of natural concepts, which normally have fuzzy boundaries, admit borderline cases, and are susceptible to Zeno's sorites paradox. We will discuss the psychology of vagueness, especially experiments investigating the judgment of borderline cases and contradictions. In the theoretical part, we will propose a probabilistic model that describes the quantitative characteristics of the experimental finding and extends Alxatib's and Pelletier's () theoretical analysis. The model is based on a Hopfield network for predicting truth values. Powerful (...)
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  • Quantum key distribution without the wavefunction.Gerd Niestegge - unknown
    A well-known feature of quantum mechanics is the secure exchange of secret bit strings which can then be used as keys to encrypt messages transmitted over any classical communication channel. It is demonstrated that this quantum key distribution allows a much more general and abstract access than commonly thought. The results include some generalizations for the Hilbert space version of quantum key distribution, but base upon a general non-classical extension of conditional probability. A special state-independent conditional probability is identifed as (...)
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