Atmanspacher, H.

Blutner, R.K.

Busemeyer, J.R.

Pothos, E.M.

Shiffrin, R.M.

Trueblood, J.S.

Wang, Z.

English

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

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UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl)UvA-DARE (Digital Academic Repository)The Potential of Quantum Probability for Modeling Cognitive ProcessesPothos, E.M.; Busemeyer, J.R.; Shiffrin, R.M.; Trueblood, J.S.; Wang, Z.; Blutner, R.K.;Atmanspacher, H.Publication date2011Document VersionFinal published versionPublished inExpanding the Space of Cognitive Science: proceedings of the 33d Annual Meeting of theCognitive Science SocietyLink to publicationCitation for published version (APA):Pothos, E. M., Busemeyer, J. R., Shiffrin, R. M., Trueblood, J. S., Wang, Z., Blutner, R. K., &Atmanspacher, H. (2011). The Potential of Quantum Probability for Modeling CognitiveProcesses. In L. Carlson, C. Hoelscher, & T. F. Shipley (Eds.), Expanding the Space ofCognitive Science: proceedings of the 33d Annual Meeting of the Cognitive Science Society:Boston, Massachusetts, July 20-23, 2011 (pp. 1336-1337). Cognitive Science Society.https://cogsci.mindmodeling.org/2011/papers/0311/index.htmlGeneral rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s)and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an opencontent license (like Creative Commons).Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, pleaselet the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the materialinaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letterto: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. Youwill be contacted as soon as possible.Download date:25 Jul 2022The 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 reseach rs 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 themechanisms which allow humans to be successful in an uncertain world. The question then becomes to identfy 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 (A&B) > Probability (A); this is the conjunction fallacy). In one-shot prisoner’s dilemma games, naïve 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 (A&B) = Probability (B&A), but QP theory does not always obey commutativity in conjunction. In QP theory probability assessment can be order (or context) dependent. Relatedly, QP theory is not constrained by the law of total probability  (though it is subject to other constraints). The law of total probability in classical theory can be expressed as Probability (A) = Probability (A&X) + Probability (A & not X), but this decomposition in QP theory may involve interference terms. As we have shown (e.g., Busemeyer et al., in press; 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 1336is the potential of such models? How well do they cover the relevant empirical findings? What are the key differences between QP theory models and matched classical probability ones? Three talks will address these issue  (Pothos  et al., Blutner, and Atmanspacher). Equally, the symposium will be an opportunity to consider concers with the applicability of QP theory. The fourth talk will cast a critical eye and address the issue of the complexity of QP models and their comparability with standard approaches.  Overview of Talks QP theory in decision making  Pothos, Busemeyer, Trueblood, & Wang. Pothos is a cognitive scientist with a background in physics. Trueblood, Wang, and Pothos have all been working with Busemeyr on QP models. Busemeyer is the mathematical psychologist who first presented to the cognitive science community detailed, formal models for psychological processes ba ed on QP theory. The talk will review the successful application of QP theory in three important empirical situations: the conjunction fallacy in Linda-type problems, order effects in human inference, and violations of the sure thing principle in Prisoner’s Dilemma.  QP theory models of semantic composition  Blutner. This speaker  is a theoretical physicist by training, interested in not only cognitive modeling, but also artificial intelligence and philosophy. He will consider a sophisticated geometrical approach for semantic composition. For example, what determines the meaning of “red nose” or “red flag”? His model will provide a solution for Quine’s problem of determining which part of anpple or grapefruit has to be red in order to call it a “red apple” or “reddish grapefruit”. The proposed quantum model is ba ed on tensor products and entangled states expressing the results of conceptual combinations. The proposal conforms to Millikan’s and Recanati’s view that comprehending language is normally as direct as the perception of visual scenery. In both cases, beliefs are formed in a direct way, apparently without reference to serial processes of inferential interpretation.  A generalized quantum framework for bistable perception Atmanspacher. This speaker, trained in theoretical physics, is the Head of the Theory and Data Analysis departmen  at the Institute for Frontier Areas of Psychology at Freiburg. He has pioneered the development of a formal framework, based on those elements of quantum theory which are considered pertinent for cognitive modeling, such as complementarity, whose historical origin can, in fact, be traced back to psychology. He will present an application for the perception of ambiguous stimuli, such as the Necker cube. The perception process is modeled as the evolution of an unstable two-state system, giving rise to a “Necker-Zeno” effect, generalizing the quantum Zeno effect to mental systems. Quantitative relations between the involved time scales are theoretically derived and found to be consistent with empirical observation. Moreover, the Necker-Zeno model predicts phenomena of temporal nonlocality, referring to mental states that are not sharply localized in time but extend over a time interval of n n-zero duration.  Model Selection applied to  QP  models  Shiffrin & Busemeyer.  Shiffrin is a cognitive psychologist with many seminal contributions to cognitive theory. With Busemeyer, he will discuss the suitability of QP theory for cognitive modeling and consider some practical issue  regarding the way QP models can be compared to traditional probability models. Do QP models fit better simply because they are more complex? Do traditional methods for mdel comparison such as Bayesian Model Selection, Minimum Description Length, and Cross Validation pose special problems when employed for quantum probability models?  These and other model selection issues will be addressed. Simulation results will be presented for some simple cases to illustrate the situation and point to potential so utions. References Baaquie, B. E. (2004) Quantum finance: Path integrals and Hamiltonians for options and interest rates. Cambridge University  Press. Busemeyer, J. R., Pothos, E. M., Franco, R., & Trueblood, J. (in press). A quantum theoretical explanation forprobability judgment errors. Psychological Review.   Baaquie, B. E. (2004) Quantum finance: Path integrals and Hamiltonians for options and interest rates. Cambridge University  Press. Busemeyer, J. R., Wang, Z., & Townsend, J. T. (2006).  Quantum dynamics of human decision-making. Journal of Mathematical Psychology, 50, 220-241. Griffiths, T. L., Chater, N., Kemp, C., Perfors, A., & Tenenbaum, J. B. (2010). Probabilistic models of cognition: exploring representations and inductive biases. Trends in Cognitive Sciences, 14, 357-364. Grover, L. K. (1997). Quantum mechanics helps in searching for a needle in a haystack. Physical Review Letters, 79, 325-328.  Oaksford, M. & Chater, N. (2007). Bayesian rationality: The probabilistic approach to human reasoning. Oxford: Oxford University Press.  Pothos, E. M. & Busemeyer, J. R. (2009). A quantum probability explanation for violations of 'rational' decision theory. Proceedings of the Royal Society B, 276, 2171-2178. Shafir, E. & Tversky, A. (1992). Thinking through uncertainty: nonconsequential reasoning and choice. Cognitive Psychology, 24, 449-474. Tversky, A., & Kahneman, D. (1983). Extensional versus intuitive reasoning: The conjunctive fallacy in probability judgment. Psychological Review, 90, 293-315. 1337

The Potential of Quantum Probability for Modeling Cognitive Processes

UvA-DARE

Pothos, Emmanuel

Busemeyer, Jerome

Shiffrin, Richard

Trueblood, Jennifer

Wang, Zheng

Blutner, Reinhard

Atmanspacher, Harald

eScholarship - University of California

UC MercedProceedings of the Annual Meeting of the Cognitive Science SocietyTitleThe Potential of Quantum Probability for Modeling Cognitive ProcessesPermalinkhttps://escholarship.org/uc/item/7b58g738JournalProceedings of the Annual Meeting of the Cognitive Science Society, 33(33)ISSN1069-7977AuthorsPothos, EmmanuelBusemeyer, JeromeShiffrin, Richardet al.Publication Date2011 Peer reviewedeScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaThe 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 reseach rs 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 themechanisms which allow humans to be successful in an uncertain world. The question then becomes to identfy 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 (A&B) > Probability (A); this is the conjunction fallacy). In one-shot prisoner’s dilemma games, naïve 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 (A&B) = Probability (B&A), but QP theory does not always obey commutativity in conjunction. In QP theory probability assessment can be order (or context) dependent. Relatedly, QP theory is not constrained by the law of total probability  (though it is subject to other constraints). The law of total probability in classical theory can be expressed as Probability (A) = Probability (A&X) + Probability (A & not X), but this decomposition in QP theory may involve interference terms. As we have shown (e.g., Busemeyer et al., in press; 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 1336is the potential of such models? How well do they cover the relevant empirical findings? What are the key differences between QP theory models and matched classical probability ones? Three talks will address these issue  (Pothos  et al., Blutner, and Atmanspacher). Equally, the symposium will be an opportunity to consider concers with the applicability of QP theory. The fourth talk will cast a critical eye and address the issue of the complexity of QP models and their comparability with standard approaches.  Overview of Talks QP theory in decision making  Pothos, Busemeyer, Trueblood, & Wang. Pothos is a cognitive scientist with a background in physics. Trueblood, Wang, and Pothos have all been working with Busemeyr on QP models. Busemeyer is the mathematical psychologist who first presented to the cognitive science community detailed, formal models for psychological processes ba ed on QP theory. The talk will review the successful application of QP theory in three important empirical situations: the conjunction fallacy in Linda-type problems, order effects in human inference, and violations of the sure thing principle in Prisoner’s Dilemma.  QP theory models of semantic composition  Blutner. This speaker  is a theoretical physicist by training, interested in not only cognitive modeling, but also artificial intelligence and philosophy. He will consider a sophisticated geometrical approach for semantic composition. For example, what determines the meaning of “red nose” or “red flag”? His model will provide a solution for Quine’s problem of determining which part of anpple or grapefruit has to be red in order to call it a “red apple” or “reddish grapefruit”. The proposed quantum model is ba ed on tensor products and entangled states expressing the results of conceptual combinations. The proposal conforms to Millikan’s and Recanati’s view that comprehending language is normally as direct as the perception of visual scenery. In both cases, beliefs are formed in a direct way, apparently without reference to serial processes of inferential interpretation.  A generalized quantum framework for bistable perception Atmanspacher. This speaker, trained in theoretical physics, is the Head of the Theory and Data Analysis departmen  at the Institute for Frontier Areas of Psychology at Freiburg. He has pioneered the development of a formal framework, based on those elements of quantum theory which are considered pertinent for cognitive modeling, such as complementarity, whose historical origin can, in fact, be traced back to psychology. He will present an application for the perception of ambiguous stimuli, such as the Necker cube. The perception process is modeled as the evolution of an unstable two-state system, giving rise to a “Necker-Zeno” effect, generalizing the quantum Zeno effect to mental systems. Quantitative relations between the involved time scales are theoretically derived and found to be consistent with empirical observation. Moreover, the Necker-Zeno model predicts phenomena of temporal nonlocality, referring to mental states that are not sharply localized in time but extend over a time interval of n n-zero duration.  Model Selection applied to  QP  models  Shiffrin & Busemeyer.  Shiffrin is a cognitive psychologist with many seminal contributions to cognitive theory. With Busemeyer, he will discuss the suitability of QP theory for cognitive modeling and consider some practical issue  regarding the way QP models can be compared to traditional probability models. Do QP models fit better simply because they are more complex? Do traditional methods for mdel comparison such as Bayesian Model Selection, Minimum Description Length, and Cross Validation pose special problems when employed for quantum probability models?  These and other model selection issues will be addressed. Simulation results will be presented for some simple cases to illustrate the situation and point to potential so utions. References Baaquie, B. E. (2004) Quantum finance: Path integrals and Hamiltonians for options and interest rates. Cambridge University  Press. Busemeyer, J. R., Pothos, E. M., Franco, R., & Trueblood, J. (in press). A quantum theoretical explanation forprobability judgment errors. Psychological Review.   Baaquie, B. E. (2004) Quantum finance: Path integrals and Hamiltonians for options and interest rates. Cambridge University  Press. Busemeyer, J. R., Wang, Z., & Townsend, J. T. (2006).  Quantum dynamics of human decision-making. Journal of Mathematical Psychology, 50, 220-241. Griffiths, T. L., Chater, N., Kemp, C., Perfors, A., & Tenenbaum, J. B. (2010). Probabilistic models of cognition: exploring representations and inductive biases. Trends in Cognitive Sciences, 14, 357-364. Grover, L. K. (1997). Quantum mechanics helps in searching for a needle in a haystack. Physical Review Letters, 79, 325-328.  Oaksford, M. & Chater, N. (2007). Bayesian rationality: The probabilistic approach to human reasoning. Oxford: Oxford University Press.  Pothos, E. M. & Busemeyer, J. R. (2009). A quantum probability explanation for violations of 'rational' decision theory. Proceedings of the Royal Society B, 276, 2171-2178. Shafir, E. & Tversky, A. (1992). Thinking through uncertainty: nonconsequential reasoning and choice. Cognitive Psychology, 24, 449-474. Tversky, A., & Kahneman, D. (1983). Extensional versus intuitive reasoning: The conjunctive fallacy in probability judgment. Psychological Review, 90, 293-315. 1337

UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl)UvA-DARE (Digital Academic Repository)The Potential of Quantum Probability for Modeling Cognitive ProcessesPothos, E.M.; Busemeyer, J.R.; Shiffrin, R.M.; Trueblood, J.S.; Wang, Z.; Blutner, R.K.;Atmanspacher, H.Publication date2011Document VersionFinal published versionPublished inExpanding the Space of Cognitive Science: proceedings of the 33d Annual Meeting of theCognitive Science SocietyLink to publicationCitation for published version (APA):Pothos, E. M., Busemeyer, J. R., Shiffrin, R. M., Trueblood, J. S., Wang, Z., Blutner, R. K., &Atmanspacher, H. (2011). The Potential of Quantum Probability for Modeling CognitiveProcesses. In L. Carlson, C. Hoelscher, & T. F. Shipley (Eds.), Expanding the Space ofCognitive Science: proceedings of the 33d Annual Meeting of the Cognitive Science Society:Boston, Massachusetts, July 20-23, 2011 (pp. 1336-1337). Cognitive Science Society.https://cogsci.mindmodeling.org/2011/papers/0311/index.htmlGeneral rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s)and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an opencontent license (like Creative Commons).Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, pleaselet the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the materialinaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letterto: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. Youwill be contacted as soon as possible.Download date:09 Mar 2023The 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 reseach rs 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 themechanisms which allow humans to be successful in an uncertain world. The question then becomes to identfy 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 (A&B) > Probability (A); this is the conjunction fallacy). In one-shot prisoner’s dilemma games, naïve 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 (A&B) = Probability (B&A), but QP theory does not always obey commutativity in conjunction. In QP theory probability assessment can be order (or context) dependent. Relatedly, QP theory is not constrained by the law of total probability  (though it is subject to other constraints). The law of total probability in classical theory can be expressed as Probability (A) = Probability (A&X) + Probability (A & not X), but this decomposition in QP theory may involve interference terms. As we have shown (e.g., Busemeyer et al., in press; 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 1336is the potential of such models? How well do they cover the relevant empirical findings? What are the key differences between QP theory models and matched classical probability ones? Three talks will address these issue  (Pothos  et al., Blutner, and Atmanspacher). Equally, the symposium will be an opportunity to consider concers with the applicability of QP theory. The fourth talk will cast a critical eye and address the issue of the complexity of QP models and their comparability with standard approaches.  Overview of Talks QP theory in decision making  Pothos, Busemeyer, Trueblood, & Wang. Pothos is a cognitive scientist with a background in physics. Trueblood, Wang, and Pothos have all been working with Busemeyr on QP models. Busemeyer is the mathematical psychologist who first presented to the cognitive science community detailed, formal models for psychological processes ba ed on QP theory. The talk will review the successful application of QP theory in three important empirical situations: the conjunction fallacy in Linda-type problems, order effects in human inference, and violations of the sure thing principle in Prisoner’s Dilemma.  QP theory models of semantic composition  Blutner. This speaker  is a theoretical physicist by training, interested in not only cognitive modeling, but also artificial intelligence and philosophy. He will consider a sophisticated geometrical approach for semantic composition. For example, what determines the meaning of “red nose” or “red flag”? His model will provide a solution for Quine’s problem of determining which part of anpple or grapefruit has to be red in order to call it a “red apple” or “reddish grapefruit”. The proposed quantum model is ba ed on tensor products and entangled states expressing the results of conceptual combinations. The proposal conforms to Millikan’s and Recanati’s view that comprehending language is normally as direct as the perception of visual scenery. In both cases, beliefs are formed in a direct way, apparently without reference to serial processes of inferential interpretation.  A generalized quantum framework for bistable perception Atmanspacher. This speaker, trained in theoretical physics, is the Head of the Theory and Data Analysis departmen  at the Institute for Frontier Areas of Psychology at Freiburg. He has pioneered the development of a formal framework, based on those elements of quantum theory which are considered pertinent for cognitive modeling, such as complementarity, whose historical origin can, in fact, be traced back to psychology. He will present an application for the perception of ambiguous stimuli, such as the Necker cube. The perception process is modeled as the evolution of an unstable two-state system, giving rise to a “Necker-Zeno” effect, generalizing the quantum Zeno effect to mental systems. Quantitative relations between the involved time scales are theoretically derived and found to be consistent with empirical observation. Moreover, the Necker-Zeno model predicts phenomena of temporal nonlocality, referring to mental states that are not sharply localized in time but extend over a time interval of n n-zero duration.  Model Selection applied to  QP  models  Shiffrin & Busemeyer.  Shiffrin is a cognitive psychologist with many seminal contributions to cognitive theory. With Busemeyer, he will discuss the suitability of QP theory for cognitive modeling and consider some practical issue  regarding the way QP models can be compared to traditional probability models. Do QP models fit better simply because they are more complex? Do traditional methods for mdel comparison such as Bayesian Model Selection, Minimum Description Length, and Cross Validation pose special problems when employed for quantum probability models?  These and other model selection issues will be addressed. Simulation results will be presented for some simple cases to illustrate the situation and point to potential so utions. References Baaquie, B. E. (2004) Quantum finance: Path integrals and Hamiltonians for options and interest rates. Cambridge University  Press. Busemeyer, J. R., Pothos, E. M., Franco, R., & Trueblood, J. (in press). A quantum theoretical explanation forprobability judgment errors. Psychological Review.   Baaquie, B. E. (2004) Quantum finance: Path integrals and Hamiltonians for options and interest rates. Cambridge University  Press. Busemeyer, J. R., Wang, Z., & Townsend, J. T. (2006).  Quantum dynamics of human decision-making. Journal of Mathematical Psychology, 50, 220-241. Griffiths, T. L., Chater, N., Kemp, C., Perfors, A., & Tenenbaum, J. B. (2010). Probabilistic models of cognition: exploring representations and inductive biases. Trends in Cognitive Sciences, 14, 357-364. Grover, L. K. (1997). Quantum mechanics helps in searching for a needle in a haystack. Physical Review Letters, 79, 325-328.  Oaksford, M. & Chater, N. (2007). Bayesian rationality: The probabilistic approach to human reasoning. Oxford: Oxford University Press.  Pothos, E. M. & Busemeyer, J. R. (2009). A quantum probability explanation for violations of 'rational' decision theory. Proceedings of the Royal Society B, 276, 2171-2178. Shafir, E. & Tversky, A. (1992). Thinking through uncertainty: nonconsequential reasoning and choice. Cognitive Psychology, 24, 449-474. Tversky, A., & Kahneman, D. (1983). Extensional versus intuitive reasoning: The conjunctive fallacy in probability judgment. Psychological Review, 90, 293-315. 1337

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The Potential of Quantum Probability for Modeling Cognitive Processes

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