Full Day Tutorial on Quantum Models of Cognition and Decision Zheng (Joyce) Wang (wang.1243@osu.edu) School of Communications, Center for Cognitive and Brain Sciences The Ohio State University, Columbus, OH 43210 USA Jerome R. Busemeyer (jbusemey@indiana.edu) Cognitive Science, Indiana University, 1101 E. 10th Street, Bloomington, IN 47405 USA Jennifer S. Trueblood (jstruebl@uci.edu) Department of Cognitive Sciences, University of California, Irvine Irvine, CA 92697 USA Keywords: classical information processing; quantum information processing; logic and mathematical foundation; Bayesian probability; quantum probability; Markov and quantum processes; quantum entanglement; quantum game theory; conceptual combinations; decision making; memory. Presenters Zheng (Joyce) Wang is an associate professor at The Ohio State University. She was Co-Editor for a special issue on quantum cognition that appeared in Topics in Cognitive Science (2013, Vol. 5 (4)). Her work on quantum cognition has been funded by NSF and AFOSR. Jerome Busemeyer is Provost Professor of Psychological and Brain Sciences at Indiana University. He is Editor of Decision and Associate Editor of Psychological Review, and was Editor of Journal of Mathematical Psychology. His research interests include decision-making and dynamic modeling. Jennifer Trueblood is an assistant professor at the University of California, Irvine. She has published articles on the topic of quantum cognition in Psychological Review and Cognitive Science. Her work on quantum cognition has been funded by NSF. General Purpose This full day tutorial is an exposition of a rapidly growing new alternative approach to building computational models of cognition and decision based on quantum theory. The cognitive revolution that occurred in the 1960’s was based on classical computational logic, and the connectionist/neural network movements of the 1970’s were based on classical dynamical systems. These classical assumptions remain at the heart of both cognitive architecture and neural network theories, and they are so commonly and widely applied that we take them for granted and presume them to be true. What are these critical but hidden assumptions upon which all traditional theories rely? Quantum theory provides a fundamentally different approach to logic, reasoning, probabilistic inference, and dynamical systems. For example, quantum logic does not follow the distributive axiom of Boolean logic; quantum probabilities do not obey the disjunctive axiom of Kolmogorov probability; quantum reasoning does not obey the principle of monotonic reasoning. It turns out that humans do not obey these restrictions either, which is why we consider a quantum approach. This tutorial will provide an exposition of the basic assumptions of classical versus quantum theories. These basic assumptions will be examined, side-by-side, in a parallel and elementary manner. The logic and mathematical foundation of classical and quantum theory will be laid out in an accessible manner that uncovers the mysteries of both theories. We will show that quantum theory provides a unified and powerful explanation for a wide variety of paradoxes found in human cognition and decision ranging from attitude, inference, causal reasoning, judgment and decision, conceptual combinations, memory recognition, and associative memory. This tutorial introduces and trains cognitive scientists on this promising new theoretical and modeling approach. Previous Tutorials and Symposia The tutorial has been presented at the Cognitive Science meetings in Nashville (2007), Washington DC (2008), Amsterdam (2009), Sopporo (2012), and Berlin (2013), with about 30 to 50 participants each time. The ratings from participants after the tutorial were all very positive. Also, this tutorial follows a symposium on quantum cognition presented at the Cognitive Science meeting 2011, and these papers appeared as a special issue in Topics in Cognitive Science. A similar tutorial was presented at the 3rd and 4th Annual Meetings on Quantum Interaction in Saarbruecken, Germany (2009) and Aberdeen, Scotland (2010) with about 40 participants, the Society for Mathematical Psychology (2012), and BRiMS (2013). Participants Background This tutorial will introduce participants to an entirely new area and no previous experience or background with quantum theory will be assumed. No background in physics is required. In fact, except for a few simple examples to motivate the idea, little or no reference to physics will be made during main part of the tutorial. What is required is an elementary background in classical logic
Full Day Tutorial on Quantum Models of Cognition and Decision Zheng (Joyce) Wang (wang.1243@osu.edu) School of Communications, Center for Cognitive and Brain Sciences The Ohio State University, Columbus, OH 43210 USA Jerome R. Busemeyer (jbusemey@indiana.edu) Cognitive Science, Indiana University, 1101 E. 10th Street, Bloomington, IN 47405 USA Jennifer S. Trueblood (jstruebl@uci.edu) Department of Cognitive Sciences, University of California, Irvine Irvine, CA 92697 USA Keywords: classical information processing; quantum information processing; logic and mathematical foundation; Bayesian probability; quantum probability; Markov and quantum processes; quantum entanglement; quantum game theory; conceptual combinations; decision making; memory. Presenters Zheng (Joyce) Wang is an associate professor at The Ohio State University. She was Co-Editor for a special issue on quantum cognition that appeared in Topics in Cognitive Science (2013, Vol. 5 (4)). Her work on quantum cognition has been funded by NSF and AFOSR. Jerome Busemeyer is Provost Professor of Psychological and Brain Sciences at Indiana University. He is Editor of Decision and Associate Editor of Psychological Review, and was Editor of Journal of Mathematical Psychology. His research interests include decision-making and dynamic modeling. Jennifer Trueblood is an assistant professor at the University of California, Irvine. She has published articles on the topic of quantum cognition in Psychological Review and Cognitive Science. Her work on quantum cognition has been funded by NSF. General Purpose This full day tutorial is an exposition of a rapidly growing new alternative approach to building computational models of cognition and decision based on quantum theory. The cognitive revolution that occurred in the 1960’s was based on classical computational logic, and the connectionist/neural network movements of the 1970’s were based on classical dynamical systems. These classical assumptions remain at the heart of both cognitive architecture and neural network theories, and they are so commonly and widely applied that we take them for granted and presume them to be true. What are these critical but hidden assumptions upon which all traditional theories rely? Quantum theory provides a fundamentally different approach to logic, reasoning, probabilistic inference, and dynamical systems. For example, quantum logic does not follow the distributive axiom of Boolean logic; quantum probabilities do not obey the disjunctive axiom of Kolmogorov probability; quantum reasoning does not obey the principle of monotonic reasoning. It turns out that humans do not obey these restrictions either, which is why we consider a quantum approach. This tutorial will provide an exposition of the basic assumptions of classical versus quantum theories. These basic assumptions will be examined, side-by-side, in a parallel and elementary manner. The logic and mathematical foundation of classical and quantum theory will be laid out in an accessible manner that uncovers the mysteries of both theories. We will show that quantum theory provides a unified and powerful explanation for a wide variety of paradoxes found in human cognition and decision ranging from attitude, inference, causal reasoning, judgment and decision, conceptual combinations, memory recognition, and associative memory. This tutorial introduces and trains cognitive scientists on this promising new theoretical and modeling approach. Previous Tutorials and Symposia The tutorial has been presented at the Cognitive Science meetings in Nashville (2007), Washington DC (2008), Amsterdam (2009), Sopporo (2012), and Berlin (2013), with about 30 to 50 participants each time. The ratings from participants after the tutorial were all very positive. Also, this tutorial follows a symposium on quantum cognition presented at the Cognitive Science meeting 2011, and these papers appeared as a special issue in Topics in Cognitive Science. A similar tutorial was presented at the 3rd and 4th Annual Meetings on Quantum Interaction in Saarbruecken, Germany (2009) and Aberdeen, Scotland (2010) with about 40 participants, the Society for Mathematical Psychology (2012), and BRiMS (2013). Participants Background This tutorial will introduce participants to an entirely new area and no previous experience or background with quantum theory will be assumed. No background in physics is required. In fact, except for a few simple examples to motivate the idea, little or no reference to physics will be made during main part of the tutorial. What is required is an elementary background in classical logic
This is the project associated with the Full Day Tutorial on Quantum Models of Cognition and Decision from the 38th Annual Conference of the Cognitive Science Society (CogSci 2016). The tutorial is an exposition of a rapidly growing new alternative approach to building computational models of cognition based on quantum theory. The cognitive revolution that occurred in the 1960’s was based on classical computational logic, and the connectionist/neural network movements of the 1970’s were based on classical dynamical systems. These classical assumptions remain at the heart of both cognitive architecture and neural network theories, and they are so commonly and widely applied that we take them for granted. Quantum theory provides a different approach to logic, reasoning, probabilistic inference, and dynamical systems. For example, quantum logic does not follow the distributive axiom of Boolean logic; quantum probabilities do not obey the disjunctive axiom of Kolmogorov probability; quantum reasoning does not obey the principle of monotonic reasoning. It turns out that humans do not obey these restrictions either, which is why we consider a quantum approach.
Half Day Tutorial on Using Quantum Probability Theory to Model Cognition Emmanuel M. Pothos (Emmanuel.pothos.1@city.ac.uk) Department of Psychology, City University London, London, EC1R 0JD, UK Zheng Wang (wang.1243@osu.edu) School of Communication, Derby Hall, The Ohio State University, Columbus, OH 43210 USA. Keywords: probability theory, Bayesian probability, quantum theory, decision making, probabilistic models. General Purpose This tutorial introduces why and how to build cognitive models using quantum probability (QP) theory. In the tutorial, we will show that QP is inherently consistent with deeply rooted psychological conceptions and intuitions. It offers a fresh conceptual framework for explaining some puzzling empirical findings of cognition, and provides a rich new source of alternative formal tools, compared to classical probability (CP) theory, for cognitive modeling. CP models, including Bayesian models, have had an enormous influence in cognitive science (e.g., Griffiths et al., 2010). Such formal models are appealing for many reasons. First, CP theory provides an integrated, coherent, self-consistent set of principles, which can be flexibly applied in any inductive inference situation. Second, such approaches are more falsifiable. Core principles of CP theory are inter-dependent, and identifying an empirical violation of one principle in a setting could invalidate the applicability of CP theory as a whole in that setting. Third, CP principles are intuitive. In the words of Laplace (1816, cited in Perfors et al., 2011), “probability theory is nothing but common sense reduced to calculation.” However, human cognition often goes against the description and prescription from CP theory. In one of the most influential empirical traditions in cognitive psychology, Kahneman, Tversky, and colleagues have reported persistent, clear violations of CP principles in decision making (e.g., Tversky & Kahneman, 1974). For example, consider the famous conjunction fallacy. Participants are told of a person, Linda, looking very much like a feminist and unlike a bank teller. Then, they are asked to judge probabilities of some events. Violating CP rules, people think the probability that Linda is a bank teller and a feminist is higher than the probability that she is just a bank teller. According to CP theory, it is a fallacy to think P(A and B)>P(A). Importantly, even when we become aware of our “fallacy,” we cannot shake off the impression that Linda is indeed more likely to be a bank teller and a feminist, than to be just a bank teller. Important findings like this have led to intense and extensive controversy about the mechanisms which guide human cognition and decision making. The inspiration for Jerome R. Busemeyer (jbusemey@indiana.edu) Psychological and Brain Sciences, Indiana University, Bloomington 47468 Indiana, USA. exploring QP theory in cognitive modeling partly arises as a way to resolve this controversy. The physical theory of quantum mechanics is a marriage between a framework for how to assign probabilities to events and assumptions regarding the nature of the physical world. We can call the former QP theory (or just quantum theory). Can it be applied outside of physics? The motivation for doing so is twofold. First, QP theory is a highly rigorous framework for probabilistic inference. It has been developed over several decades by some of the most brilliant scientists of all time (e.g., Bohr, Dirac, von Neumann, Planck) and has been intensely scrutinized ever since. Thus, the application of QP theory in cognitive modeling has exactly the same formal advantages as that of CP theory. Second, quantum theory allows us to consider the possible relevance in cognitive modeling of several novel concepts. For example, in quantum theory, a cognitive system can be in a superposition state. This means that relative to a question or measurement, the system is in an indefinite state, with all definite states having potential to be expressed. This provides an intrinsic formal representation of the conflict, ambiguity, or uncertainty that people experience in cognitive processes. For another example: states can be entangled, which means a change in one part of the system inexorably and instantaneously affects another part. Entanglement is a form of extreme association, which can be helpful for formalizing important cognitive processes, such as holism, cognitive dissonance, and social projection. Fundamental quantum conceptions, such as superposition, entanglement, interference, and complementarity, have no formal counterparts in cognitive theory. We are part of a growing group of researchers who have been intensely exploring their applicability in understanding human cognition. Quantum theory reveals alternative intuitions in probabilistic models of cognition. The quantum cognition research program aims to explore whether these alternative intuitions can explain paradoxical findings in decision, memory, and other areas of cognitive processing. The tutorial introduce the basic principles of quantum theory, in the context of well-known empirical findings in psychological literature. The basic elements of QP theory will require only some knowledge of linear algebra. No background in physics or quantum theory is assumed. The tutorial will be self-contained. It will show how probability
The Potential of Quantum Probability for Modeling Cognitive Processes Emmanuel M. Pothos (e.m.pothos@swansea.ac.uk) Department of Psychology, Swansea University, SA2 8PP, UK Jerome R. Busemeyer (jbusemey@indiana.edu), Richard M. Shiffrin (shiffrin@indiana.edu), Jennifer S. Trueblood (jstruebl@indiana.edu) Department of Psychological and Brain Sciences, Indiana University, Bloomington 47468, USA. Zheng Wang (wang.1243@osu.edu) Ohio State University, School of Communication, Columbus 43210, USA. Reinhard K. Blutner (reinhard@blutner.de) Institute of Logic, Language, and Computation, University of Amsterdam, 1090 GE Amsterdam, The Netherlands. Harald Atmanspacher (atmanspacher@collegium.ethz.ch) Department of Theory and Data Analysis, IGPP, D-79098 Freiburg, Germany. Keywords: Quantum probability, formal approaches, decision making, conceptual combination General Background and Speakers Quantum probability (QP) theory is a theory for how to assign probabilities to observables. In the context of physics, it has been successfully employed by researchers for over 100 years and has been the basis for some of the most impressive discoveries of the human mind (e.g., the transistor, and so the microchip, and the laser). But the applicability of QP theory is not limited to physical phenomena and, indeed, there has been growing interest in exploring the potential of QP theory in areas as diverse as economics (Baaquie, 2004), information theory (e.g., Grover, 1997), and psychology. We are interested in the latter objective. Probabilistic approaches to cognition have been recently enjoying considerable success (e.g., Griffiths et al., 2010). This is perhaps unsurprising. Several (if not most) aspects of cognitive processing involve inference about quantities which cannot be determined with certainty. Thus, probability theory seems an ideal tool for formalizing uncertainty in cognitive processes and describing the mechanisms which allow humans to be successful in an uncertain world. The question then becomes to identify the probabilistic framework which is most suitable for modeling particular aspects of cognition. Cognitive scientists have widely employed classical probability theory and there is no doubt that such approaches can be incredibly successful for particular problems (e.g., Oaksford & Chater, 2007). But is Bayesian probability always the most suitable probabilistic framework for describing cognitive processes? Human inference often appears to violate fundamental laws of classical probability. For example, in the famous Linda problem of Tversky and Kahneman (1983) participants consider as more likely a conjunctive statement than a corresponding single premise one (i.e., Probability (AB this is the conjunction fallacy). In one-shot prisoner’s dilemma games, naive participants choose to defect knowing their opponent defects, they choose to also defect knowing their opponent cooperates, but they reverse their judgment and choose to cooperate when their opponent’s action is unknown (Shafir & Tversky, 1992). This result is also hard to reconcile with classical probability theory, it violates the sure thing principle and the law of total probability. Findings such as the conjunction fallacy and the violation of the sure thing principle provide the motivation for exploring probabilistic frameworks alternative to classic probability theory. QP theory is mostly consistent with classical probability theory, but for a crucial difference. In classical probability theory Probability (AB Busemeyer, Wang, & Townsend, 2006; Pothos & Busemeyer, 2009), these properties of QP theory can lead to successful and simple QP models for empirical findings, such as the conjunction fallacy and the violation of the sure thing principle. Finally, QP theory remains suitable for describing cognition without involving any claim that the brain is a quantum computer. Rather, we adopt what is a standard approach in cognitive science and ask: 'does quantum probability theory produce results which predict human behavior well?’ The application of QP theory in cognition holds a lot of promise. The main objective of this symposium is to present the key ideas to the cognitive science community and summarize progress with QP theory cognitive models. What
Much of our understanding of human thinking is based on probabilistic models. This innovative book by Jerome R. Busemeyer and Peter D. Bruza argues that, actually, the underlying mathematical structures from quantum theory provide a much better account of human thinking than traditional models. They introduce the foundations for modeling probabilistic-dynamic systems using two aspects of quantum theory. The first, 'contextuality', is a way to understand interference effects found with inferences and decisions under conditions of uncertainty. The second, 'quantum entanglement', allows cognitive phenomena to be modeled in non-reductionist ways. Employing these principles drawn from quantum theory allows us to view human cognition and decision in a totally new light. Introducing the basic principles in an easy-to-follow way, this book does not assume a physics background or a quantum brain and comes complete with a tutorial and fully worked-out applications in important areas of cognition and decision.
The paper "What Is Quantum Cognition, and How Is It Applied to Psychology?" by Busemeyer and Wang (2015) introduces the concept of quantum cognition as a framework for understanding human cognition in psychology.This critical analysis aims to evaluate the key arguments and contributions presented in the paper.The authors propose quantum cognition as a research program that utilizes mathematical principles from quantum theory to explain various aspects of human cognition, such as judgment, decision-making, concepts, reasoning, memory, and perception.They emphasize that quantum cognition does not focus on whether the brain is a quantum computer, but rather utilizes quantum theory as a fresh conceptual framework and a set of formal tools for elucidating empirical findings in psychology.The authors specifically highlight two quantum principles, complementarity, and superposition, to demonstrate the potential of quantum cognition as a theoretical direction for psychology.Complementarity suggests that some psychological measures need to be made sequentially, where the context generated by the first measure can influence responses to the next one, leading to measurement order effects.Superposition suggests that certain psychological states cannot be defined by definite values, but rather encompass a range of potential expressions.This critical review will analyze the strengths and weaknesses of the arguments presented by Busemeyer and Wang, evaluate the evidence supporting their claims, and discuss the implications of quantum cognition for the field of psychology.
Quantum Models of Cognition and Decision, Second Edition presents a fully updated and expanded version of this innovative and path-breaking text. It offers an accessible introduction to the intersection of quantum theory and cognitive science, covering new insights, modelling techniques, and applications for understanding human cognition and decision making. In it, Busemeyer and Bruza delve into such topics as the non-commutative nature of judgments, quantum interference as a general principle governing human decision making, contextuality in modelling human cognition, and thought-provoking speculation about what a quantum approach to cognition might reveal about the ultimate nature of the human mind. Additions include new material on measurement, open systems, and applications to computer science. Requiring no prior background in quantum physics, this book comes complete with a tutorial and fully worked-out applications in important areas of cognition and decision.