Statistical and subjective interpretations of probability in quantum-like models of cognition and decision making
Statistical and subjective interpretations of probability in quantum-like models of cognition and decision making
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DOI：
10.1016/j.jmp.2016.02.005
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发表时间：
2016-10-01
影响因子：
1.8
通讯作者：
Khrennikov, Andrei
中科院分区：
文献类型：
--
作者：
Haven, Emmanuel;Khrennikov, Andrei
本文首先介绍了经典概率的基本数学模型，即Kolmogorov（1933）测度论模型。它的两个基本解释进行了讨论：统计和主观。然后，我们提出了量子力学（QM）的概率结构，并讨论了量子态的解释问题和玻恩规则给出的相应概率。量子概率（QP）在认知和决策（DM）建模中的应用与量子概率（QM）面临着相同的解释问题。这里的情况甚至比物理学中的情况更复杂。我们分析了使用主观和统计解释的QP的优点和缺点。在量子贝叶斯主义（QBism）的框架下，QP的主观方法被形式化，这是C。Fuchs和他的合作者。QP的统计方法在QM的各种解释中提出，无论是在不现实的解释中，例如，哥本哈根解释（最新版本由A. Plotnitsky），并在现实的解释（例如，最近的瓦克舍解释）。目前，我们不能作出肯定的选择，赞成任何解释。因此，类量子DM面临着与量子物理学相同的解释问题。(C)2016 Elsevier Inc. All rights reserved.
The paper starts with an introduction to the basic mathematical model of classical probability (CP), i.e. the Kolmogorov (1933) measure-theoretic model. Its two basic interpretations are discussed: statistical and subjective. We then present the probabilistic structure of quantum mechanics (QM) and discuss the problem of interpretation of a quantum state and the corresponding probability given by Born's rule. Applications of quantum probability (QP) to modeling of cognition and decision making (DM) suffer from the same interpretational problems as QM. Here the situation is even more complicated than in physics. We analyze advantages and disadvantages of the use of subjective and statistical interpretations of QP. The subjective approach to QP was formalized in the framework of Quantum Bayesianism (QBism) as the result of efforts from C. Fuchs and his collaborators. The statistical approach to QP was presented in a variety of interpretations of QM, both in nonrealistic interpretations, e.g., the Copenhagen interpretation (with the latest version due to A. Plotnitsky), and in realistic interpretations (e.g., the recent Vaxjo interpretation). At present, we cannot make a definite choice in favor of any of the interpretations. Thus, quantum-like DM confronts the same interpretational problem as quantum physics does. (C) 2016 Elsevier Inc. All rights reserved.