Quantum cognition

Quantum cognition is an emerging field which applies the formalism of quantum theory to model cognitive phenomena such as human memory, concepts and conceptual reasoning, human judgment, and decision making. The field clearly distinguishes itself from the Quantum mind as it is not reliant on the hypothesis that there is something quantum mechanical about the brain.

Quantum cognition uses only the mathematical basis of quantum theory to inspire and formalize models of cognition that are superior to models based on traditional probability theory. ``Superior” means a closer fit to empirical data and/or increased explanatory power. The field focuses on modeling phenomena in cognitive science which have stubbornly resisted traditional modeling techniques or where traditional models seem to have reached a barrier (e.g., human memory). A few brief examples are provided below.

Contents

Examples

Decision making – Suppose a person is given a chance to play the following gamble twice: an even chance to win $200 or lose $100. If they think they won the first play, or alternatively if they think they lost the first play, then the majority chooses to play again on the second round. Given these preferences, according to the sure thing principle of rational decision theory, they should also play the second round even if they don’t know or think about the outcome of the first round.[1] Yet the majority of people do just the opposite in the latter case.[2] This finding violates the law of total probability, yet it can be explained as a quantum interference effect in a manner similar to the explanation for the results from two-hole experiments in physics.[3][4][5]

Human probability judgments – Quantum probability provides a new way to explain human probability judgment errors including the conjunction and disjunction errors.[6] A conjunction error occurs when a person judges the probability of a likely event L and an unlikely event U to be greater than the unlikely event U; a disjunction error occurs when a person judges the probability of a likely event L to be greater than the probability of the likely event L or an unlikely event U. Quantum probability theory is a generalization of Bayesian probability theory because it is based on a set of von Neumann axioms that relax some of the classic Kolmogorov axioms. The quantum model introduces a new fundamental concept to cognition—the compatibility versus incompatibility of questions and the effect this can have on the sequential order of judgments. Quantum probability provides a simple account of conjunction and disjunction errors as well as many other findings such as order effects on probability judgments[5][7]

Concepts – Concepts are basic cognitive phenomena, which provide the content for inference, explanation, and language understanding. Cognitive psychology has researched different approaches for understanding concepts including exemplars, prototypes, and neural networks, and different fundamental problems have been identified, such as the experimentally tested non classical behavior for the conjunction and disjunction of concepts, more specifically the Pet-Fish problem or guppy effect,[8] and the overextension and underextension of typicality and membership weight for conjunction and disjunction.[9] By and large, quantum cognition has drawn on quantum theory in three ways to model concepts.

  1. Exploit the contextuality of quantum theory to account for the contextuality of concepts in cognition and language and the phenomenon of emergent properties when concepts combine [10][11][12][13]
  2. Use quantum entanglement to model the semantics of concept combinations in a non-decompositional way, and to account for the emergent properties/associates/inferences in relation to concept combinations[14]
  3. Use quantum superposition to account for the emergence of a new concept when concepts are combined, and as a consequence put forward an explanatory model for the Pet-Fish problem situation, and the overextension and underextension of membership weights for the conjunction and disjunction of concepts.[10][11][15]

Human memory – Speculation that there may be something quantum-like about the human mental lexicon began with “Spooky Activation at Distance” formula which attempted to model the intuition that when a word’s associative network is activated during study in memory experiment, it behaves like a quantum-entangled system.[16]

History

There is a short, but significant history of applying the formalisms of quantum theory to topics in psychology. Initial ideas for applying quantum formalisms to cognition first appeared in the 1990s by Diederik Aerts, Harald Atmanspacher, Robert Bordley, and Andrei Khrennikov (see additional reading). Ten years later, there appeared many more detailed empirical applications (see additional reading). A special issue on “Quantum Cognition and Decision” appeared in the Journal of Mathematical Psychology (2009, vol 53.), which planted a flag for the field. Two books closely related to quantum cognition were recently published by Khrennikov (2010) and Ivancivic and Ivancivic (2010), and a new book on quantum cognition and decision is being prepared by Busemeyer and Bruza. The first Quantum Interaction workshop was held at Stanford in 2007 organized by Peter Bruza, William Lawless, C. J. van Rijsbergen, and Don Sofge as part of the 2007 AAAI Spring Symposium Series. This first workshop was followed by workshops at Oxford (England) in 2008, Saarbruken (Germany) in 2009, and most recently at the 2010 AAAI Fall Symposium Series held in Washington DC. The next workshop will take place in Aberdeen, Scotland 26–29 June 2011. Tutorials also were presented annually beginning in 2007 until 2009 at the meeting of the Cognitive Science Society.

Links

References

  1. ^ Savage, L. J. The Foundations of Statistics: John Wiley & Sons. 1954
  2. ^ Tversky, A., Shafir, E. The disjunction effect in choice under uncertainty. Psychological Science 1992; 3: 305-309.
  3. ^ Khrennikov, A. Y. (2010) Ubiquitous quantum structure. Springer.
  4. ^ Pothos, E. M. & Busemeyer, J. R. (2009) A quantum probability model explanation for violations of ‘rational’ decision theory. Proceedings of the Royal Society, B, 276 (1665), 2171-2178.
  5. ^ a b Yukalov, V., & Sornette, D. (2010). Decision theory with prospect interference and entanglement. Theory and Decision, 1-46
  6. ^ Tversky, A., & Kahneman, D. (1983). Extensional versus intuitive reasoning: The conjuctive fallacy in probability judgment. Psychological Review, 90, 293-315
  7. ^ Busemeyer, J. R., Pothos, E. & Franco, R., (in press) A quantum theoretical explanation for probability judgment ‘errors’. Psychological Review
  8. ^ Osherson, D. N. and Smith, E. E. (1981). On the adequacy of prototype theory as a theory of concepts. Cognition, 9, 35–58
  9. ^ Hampton, J. A. (1988). Overextension of conjunctive concepts: Evidence for a unitary model for concept typicality and class inclusion. Journal of Experimental Psychology: Learning, Memory, and Cognition, 14, 12–32
  10. ^ a b Aerts, D. & Gabora, L. (2005). A state-context-property model of concepts and their combinations I: The structure of the sets of contexts and properties. Kybernetes, 34(1&2), 167-191.
  11. ^ a b Aerts, D. & Gabora, L. (2005). A state-context-property model of concepts and their combinations II: A Hilbert space representation. Kybernetes, 34(1&2), 192-221.
  12. ^ Gabora, L. & Aerts, D. (2002). Contextualizing concepts using a mathematical generalization of the quantum formalism. Journal of Experimental and Theoretical Artificial Intelligence, 14(4), 327-358.
  13. ^ Widdows, D. & Peters, S. (2003). Word Vectors and Quantum Logic: Experiments with negation and disjunction. Eighth Mathematics of Language Conference, 141-154.
  14. ^ Bruza, P.D. & Cole, R.J. (2005). Quantum logic of semantic space: An exploratory investigation of context effects in practical reasoning In S. Artemov, H. Barringer, A. S. d'Avila Garcez, L.C. Lamb, J. Woods (eds.) We Will Show Them: Essays in Honour of Dov Gabbay. College Publications.
  15. ^ Aerts, D. (2009). Quantum structure in cognition. Journal of Mathematical Psychology, 53, 314-348.
  16. ^ Bruza, P., Kitto, K., Nelson, D., & McEvoy, C. (2009) Is there something quantum-like in the human mental lexicon? Journal of Mathematical Psychology,53,362-377.

Additional Reading