Abstract
This review paper has three main goals. First, to discuss a contextual neurophysiologically plausible model of neural oscillators that reproduces some of the features of quantum cognition. Second, to show that such a model predicts contextual situations where quantum cognition is inadequate. Third, to present an extended probability theory that not only can describe situations that are beyond quantum probability, but also provides an advantage in terms of contextual decision-making.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abramsky, S., & Brandenburger, A. (2011). The sheaf-theoretic structure of non-locality and contextuality. New Journal of Physics, 13(11), 113036.
Abramsky, S., & Brandenburger, A. (2014). An operational interpretation of negative probabilities and no-signalling models. In F. van Breugel, E. Kashefi, C. Palamidessi, & J. Rutten (Eds.), Horizons of the mind. A tribute to Prakash Panangaden. Lecture notes in computer science (Vol. 8464, pp. 59–75). Berlin: Springer International Publisher.
Aerts, D. (2009). Quantum structure in cognition. Journal of Mathematical Psychology, 53(5), 314–348.
Aerts, D., Broekaert, J., Gabora, L., & Veloz, T. (2012). The guppy effect as interference. In J. R. Busemeyer, F. Dubois, A. Lambert-Mogiliansky, & M. Melucci (Eds.), Quantum interaction. Lecture notes in computer science (Vol. 7620, pp. 36–47). Berlin, Heidelberg: Springer.
Aerts, D., & Sozzo, S. (2014). Quantum entanglement in concept combinations. International Journal of Theoretical Physics, 53(10), 3587–3603.
Al-Safi, S. W., & Short, A. J. (2013). Simulating all nonsignaling correlations via classical or quantum theory with negative probabilities. Physical Review Letters, 111(17), 170403.
Anand, P., Pattanaik, P., & Puppe, C. (Eds.). (2009). The handbook of rational and social choice: An overview of new foundations and applications. Oxford, England: Oxford University Press.
Ashtiani, M., & Azgomi, M. A. (2015). A survey of quantum-like approaches to decision making and cognition. Mathematical Social Sciences, 75, 49–80.
Aspect, A., Dalibard, J., & Roger, G. (1982). Experimental test of bell’s inequalities using time-varying analyzers. Physical Review Letters, 49(25), 1804–1807.
Aspect, A., Grangier, P., & Roger, G. (1981). Experimental tests of realistic local theories via bell’s theorem. Physical Review Letters, 47(7), 460–463.
Atmanspacher, H., & Römer, H. (2012). Order effects in sequential measurements of non-commuting psychological observables. Journal of Mathematical Psychology, 56(4), 274–280.
Bell, J. S. (1964). On the Einstein-Podolsky-Rosen paradox. Physics, 1(3), 195–200.
Bell, J. S. (1966). On the problem of hidden variables in quantum mechanics. Reviews of Modern Physics, 38(3), 447–452.
Bell, J. S. (2004). Speakable and unspeakable in quantum mechanics: Collected papers on quantum philosophy. Cambridge: Cambridge University Press.
Boole, G. (1854). An investigation of the laws of thought: On which are founded the mathematical theories of logic and probabilities. New York: Dover Publications.
Briggs, R. (2015). Normative theories of rational choice: Expected utility. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Winter 2015 edition). http://plato.stanford.edu/archives/win2015/entries/rationality-normative-utility/.
Busemeyer, J. R., & Bruza, P. D. (2012). Quantum models of cognition and decision. Cambridge: Cambridge University Press.
Busemeyer, J. R., & Diederich, A. (2010). Cognitive modeling. Thousand Oaks: SAGE.
Busemeyer, J. R., Pothos, E. M., Franco, R., & Trueblood, J. S. (2011). A quantum theoretical explanation for probability judgment errors. Psychological Review, 118(2), 193–218.
Busemeyer, J. R., Wang, Z., Khrennikov, A., & Basieva, I. (2014). Applying quantum principles to psychology. Physica Scripta, 2014(T163), 014007.
Busemeyer, J. R., Wang, Z., & Townsend, J. T. (2006). Quantum dynamics of human decision-making. Journal of Mathematical Psychology, 50(3), 220–241.
Cabello, A. (2011). Quantum physics: Correlations without parts. Nature, 474(7352), 456–458.
Cabello, A. (2013). Simple explanation of the quantum violation of a fundamental inequality. Physical Review Letters, 110(6), 060402.
Cabello, A. (2014). The exclusivity principle singles out the quantum violation of the bell inequality. arXiv:1406.5656 [quant-ph]. arXiv: 1406.5656.
Clauser, J. F., Horne, M. A., Shimony, A., & Holt, R. A. (1969). Proposed experiment to test local hidden-variable theories. Physical Review Letters, 23(15), 880–884.
Collins, A. M., & Loftus, E. F. (1975). A spreading-activation theory of semantic processing. Psychological Review, 82(6), 407–428.
Cox, R. T. (1961). The algebra of probable inference. Baltimore: The John Hopkins Press.
de Barros, J. A. (2012). Joint probabilities and quantum cognition. In A. Khrennikov, A. L Migdall, S. Polyakov, & H. Atmanspacher (Eds.), AIP conference proceedings, Vaxjo, Sweden, December 2012 (Vol. 1508, pp. 98–107). American Institute of Physics.
de Barros, J. A. (2012). Quantum-like model of behavioral response computation using neural oscillators. Biosystems, 110(3), 171–182.
de Barros, J. A. (2014). Decision making for inconsistent expert judgments using negative probabilities. In Quantum interaction. Lecture notes in computer science (pp. 257–269). Berlin/Heidelberg: Springer.
de Barros, J. A. (2015). Beyond the quantum formalism: Consequences of a neural-oscillator model to quantum cognition. In H. Liljenström (Ed.), Advances in cognitive neurodynamics (IV). Advances in cognitive neurodynamics (pp. 401–404). Netherlands: Springer.
de Barros, J. A., Dzhafarov, E. N., Kujala, J. V., & Oas, G. (2015). Measuring observable quantum contextuality. In International symposium on quantum interaction (pp. 36–47). Dordrecht: Springer International Publishing.
de Barros, J. A., & Oas, G. (2014). Response selection using neural phase oscillators. In C. E. Crangle, A. G. de la Sienra, & H. E. Logino (Eds.), Foundations and methods from mathematics to neuroscience: Essays inspired by Patrick Suppes. Stanford, CA: CSLI Publications, Stanford University.
de Barros, J. A., & Oas, G. (2014). Negative probabilities and counter-factual reasoning in quantum cognition. Physica Scripta, T163, 014008.
de Barros, J. A., Oas, G., & Suppes, P. (2015). Negative probabilities and counterfactual reasoning on the double-slit experiment. In J.-Y. Beziau, D. Krause, & J. B. Arenhart (Eds.), Conceptual clarification: Tributes to Patrick Suppes (1992–2014). London: College Publications.
de Barros, J. A., & Suppes, P. (2009). Quantum mechanics, interference, and the brain. Journal of Mathematical Psychology, 53(5), 306–313.
De Morgan, A. (1910). On the study and difficulties of mathematics. La Salle: Open Court Publishing Company.
Dieks, D. (1982). Communication by EPR devices. Physics Letters A, 92(6), 271–272.
Dirac, P. A. M. (1942). Bakerian lecture. The physical interpretation of quantum mechanics. Proceedings of the Royal Society of London B, A180, 1–40.
Dzhafarov, E. N., & Kujala, J. N. (2014). A qualified Kolmogorovian account of probabilistic contextuality. In Quantum interaction. Lecture notes in computer science (Vol. 8369, pp. 201–212).
Dzhafarov, E. N., & Kujala, J. V. (2013). All-possible-couplings approach to measuring probabilistic context. PLoS ONE, 8(5), e61712.
Dzhafarov, E. N., & Kujala, J. V. (2014). Contextuality in generalized Klyachko-type, bell-type, and Leggett-Garg-type systems. arXiv:1411.2244 [physics, physics:quant-ph]. arXiv: 1411.2244.
Dzhafarov, E. N., & Kujala, J. V. (2014). Contextuality is about identity of random variables. Physica Scripta, 2014(T163), 014009.
Dzhafarov, E. N., & Kujala, J. V. (2015). Random variables recorded under mutually exclusive conditions: Contextuality-by-default. In Advances in cognitive neurodynamics (IV) (pp. 405–409). The Netherlands: Springer.
Dzhafarov, E. N., Kujala, J. V., & Larsson, J. Å. (2015). Contextuality in three types of quantum-mechanical systems. Foundations of Physics, 45(7), 762–782.
Einstein, A., Podolsky, B., & Rosen, N. (1935). Can quantum-mechanical description of physical reality be considered complete? Physical Review, 47(10), 777–780.
Feynman, R. P. (1987). Negative probability. In B. J. Hiley & F. D. Peat (Eds.), Quantum implications: Essays in honour of David Bohm (pp. 235–248). London and New York: Routledge.
Feynman, R. P., Leighton, R. B., & Sands, M. L. (2011). The Feynman lectures on physics: Mainly mechanics, radiation, and heat (Vol. 3). New York, NY: Basic Books.
Fine, A. (1982). Hidden variables, joint probability, and the bell inequalities. Physical Review Letters, 48(5), 291–295.
Fine, A. (1982). Some local models for correlation experiments. Synthese, 50(2), 279–294.
Fine, A. (2009). The shaky game. Chicaco: University of Chicago Press.
Galavotti, M. C. (2005). Philosophical introduction to probability. CSLI lecture notes (Vol. 167). Stanford, CA: CSLI Publications.
Gühne, O., Budroni, C., Cabello, A., Kleinmann, M., & Larsson, J.-Å. (2014). Bounding the quantum dimension with contextuality. Physical Review A, 89(6), 062107.
Halliwell, J. J., & Yearsley, J. M. (2013). Negative probabilities, fine’s theorem, and linear positivity. Physical Review A, 87(2), 022114.
Haven, E., & Khrennikov, A. (2013). Quantum social science. Cambridge: Cambridge University Press.
Haven, E., & Khrennikov, A. (2015). A brief introduction to quantum formalism. In E. Haven & A. Khrennikov (Eds.), The Palgrave handbook of quantum models in social science: Applications and grand challenges. New York: Palgrave MacMillan.
Holik, F., Saenz, M., & Plastino, A. (2014). A discussion on the origin of quantum probabilities. Annals of Physics, 340(1), 293–310.
Izhikevich, E. M. (2007). Dynamical systems in neuroscience: The geometry of excitability and bursting. Cambridge, MA: The MIT Press.
Jaynes, E. T. (2003). Probability theory: The logic of science. Cambridge, Great Britain: Cambridge University Press.
Jeffrey, R. (1992). Probability and the art of judgment. Cambridge, UK: Cambridge University Press.
Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica: Journal of the Econometric Society, 47(2), 263–291.
Khrennikov, A. (1993). p-Adic probability theory and its applications. {T}he principle of statistical stabilization of frequencies. Theoretical and Mathematical Physics, 97(3), 1340–1348.
Khrennikov, A. (1993). p-Adic statistical models. Doklady Akademii Nauk, 330(3), 300–304.
Khrennikov, A. Y. (1993). Statistical interpretation of p-adic valued quantum field theory. Doklady Akademii Nauk-Rossijskaya Akademiya Nauk, 328(1), 46–49.
Khrennikov, A. (1994). Discrete Qp-valued probabilities. Russian Academy of Sciences-Doklady Mathematics-AMS Translation, 48(3), 485–490.
Khrennikov, A. (1994). p-Adic valued distributions in mathematical physics. Mathematics and its applications (Vol. 309). Dordrecht, Holland: Springer Science+Business Media.
Khrennikov, A. (2009). Interpretations of probability. Berlin: Walter de Gruyter.
Khrennikov, A. (2010). Ubiquitous quantum structure. Heidelberg: Springer.
Khrennikov, A., Basieva, I., Dzhafarov, E. N., & Busemeyer, J. R. (2014). Quantum models for psychological measurements: An unsolved problem. PLoS ONE, 9(10), e110909.
Kochen, S., & Specker, E. P. (1967). The problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics, 17, 59–87.
Kochen, S., & Specker, E. P. (1975). The problem of hidden variables in quantum mechanics. In C. F. Hooker (Ed.), The logico-algebraic approach to quantum mechanics (pp. 293–328). Dordrecht, Holland: D. Reidel Publishing Co.
Kolmogorov, A. N. (1956). Foundations of the theory of probability (2nd ed.). Oxford, England: Chelsea Publishing Co.
Kuramoto, Y. (1984). Chemical oscillations, waves, and turbulence. Mineola, NY: Dover Publications, Inc.
Loubenets, E. R. (2015). Context-invariant quasi hidden variable (qHV) modelling of all joint von Neumann measurements for an arbitrary hilbert space. Journal of Mathematical Physics, 56(3), 032201.
Mückenheim, G. (1986). A review of extended probabilities. Physics Reports, 133(6), 337–401.
Oas, G., Acacio de Barros, J., & Carvalhaes, C. (2014). Exploring non-signalling polytopes with negative probability. Physica Scripta, T163, 014034.
Pais, A. (1986). Inward bound: Of matter and forces in the physical world. Oxford, UK: Oxford University Press.
Peres, A. (1995). Quantum theory: Concepts and methods. New York: Springer Science & Business Media.
Pothos, E. M., & Busemeyer, J. R. (2009). A quantum probability explanation for violations of “rational” decision theory. Proceedings of the Royal Society B: Biological Sciences, 276(1665), 2171–2178.
Ruzsa, I. Z., & Székely, G. J. (1983). Convolution quotients of nonnegative functions. Monatshefte für Mathematik, 95(3), 235–239.
Savage, L. J. (1972). The foundations of statistics, 2nd ed. Mineola, NY: Dover Publications Inc.
Shafir, E., & Tversky, A. (1992). Thinking through uncertainty: Nonconsequential reasoning and choice. Cognitive Psychology, 24(4), 449–474.
Suppes, P. (2002). Representation and invariance of scientific structures. Stanford, CA: CSLI Publications.
Suppes, P., & Atkinson, R. C. (1960). Markov learning models for multiperson interactions. Stanford, CA: Stanford University Press.
Suppes, P., & de Barros, J. A. (1996). Photons, billiards and chaos. In P. Weingartner & G. Schurz (Eds.), Law and prediction in the light of chaos research (Vol. 473, pp. 189–201). Berlin, Heidelberg: Springer.
Suppes, P., de Barros, J. A., & Oas, G. (2012). Phase-oscillator computations as neural models of stimulus–response conditioning and response selection. Journal of Mathematical Psychology, 56(2), 95–117.
Suppes, P., & Zanotti, M. (1981). When are probabilistic explanations possible? Synthese, 48(2), 191–199.
Székely, G. J. (2005). Half of a coin: Negative probabilities. Wilmott Magazine, 50, 66–68.
Trueblood, J. S., & Busemeyer, J. R. (2011). A quantum probability account of order effects in inference. Cognitive Science, 35(8), 1518–1552.
Tversky, A., & Shafir, E. (1992). The disjunction effect in choice under uncertainty. Psychological Science, 3(5), 305–309.
Wang, Z., & Busemeyer, J. R. (2013). A quantum question order model supported by empirical tests of an a priori and precise prediction. Topics in Cognitive Science, 5(4), 689–710.
Yang, D. (2006). A simple proof of monogamy of entanglement. Physics Letters A, 360(2), 249–250.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Copyright information
© 2017 The Author(s)
About this chapter
Cite this chapter
de Barros, J.A., Oas, G. (2017). Quantum Cognition, Neural Oscillators, and Negative Probabilities. In: Haven, E., Khrennikov, A. (eds) The Palgrave Handbook of Quantum Models in Social Science. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-137-49276-0_10
Download citation
DOI: https://doi.org/10.1057/978-1-137-49276-0_10
Published:
Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-1-137-49275-3
Online ISBN: 978-1-137-49276-0
eBook Packages: Economics and FinanceEconomics and Finance (R0)