Skip to main content
SpringerLink
Log in

Purposeful Choice and Point-of-View

A Generalized Quantum Approach

  • Conference paper
  • First Online:
Quantum Interaction (QI 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8369))

Included in the following conference series:

Abstract

This paper presents a generalized quantum model for describing purposes or goals of individual agents, and the way choices can be made that enable these goals to be achieved. The underlying model is a semantic vector space model, which is turned into a purposeful choice model by labelling some axes as objectives, and describing choices as transformations on the vector spaces that enable agents in the model to set these objective axes in sight.

We introduce this framework using a simplified example model of a dog trying to get food. Many parts of what has become the standard generalized quantum toolkit become apparent in this model, including learning, superposition, the importance of the metric used for normalization, classification, and a generalized uncertainty principle. The incorporation of purpose or goal into semantic vectors models also enables the analysis of traditional areas that are relatively new to artificial intelligence, including rhetoric, political science, and some of the philosophical questions touched by quantum theorists.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The claim that there is no loss at all to existing priorities when a new axis is considered is strictly true only in the continuous limit. For example, using the standard polar-coordinates parametrization where \(x = \cos (\theta )\) and \(y = \sin (\theta )\), when \(\theta = 0\), \(x = 1\), \(y = 0\), \(\frac{dy}{d\theta } = 1\) and \(\frac{dx}{d\theta } = 0\). In practice, we assume that all models will be quantized, and so to make an actual change, there will be some very small cost. The issues involved in quantizing vector models of information and cognition is not a focus of this paper: we note briefly that this example implies that it is advantageous for the smallest ‘representational quantum’ to be small.

  2. 2.

    The difference between normalized coordinates of evenly-balanced vectors using Manhattan and Euclidean metrics is greatest in dimension 4. The proof is elementary, and consists of finding \(x \in [0, 1]\) such that \(f(x) = \sqrt{x} - x\) is maximized, so \(f'(x) = \frac{x^{-\frac{1}{2}}}{2} - 1 = 0\), implying \(x^\frac{1}{2} = \frac{1}{2}\) and so \(x = \frac{1}{4}\). We are not sure if this number has any special significance.

  3. 3.

    Simulations demonstrate that a system with Euclidean normalization is more open to learning and, depending on the distribution of “food opportunities”, gets to eat more food in the long run. These results are however quite preliminary: please contact the author for more details.

References

  1. Cohen, T., Widdows, D., de Vine, L., Schvaneveldt, R., Rindflesch, T.C.: Many paths lead to discovery: analogical retrieval of cancer therapies. In: [37]

    Google Scholar 

  2. van Rijsbergen, K.: The Geometry of Information Retrieval. Cambridge University Press, Cambridge (2004)

    Book  MATH  Google Scholar 

  3. Busemeyer, J., Bruza, P.D.: Quantum models of cognition and decision. Cambridge University Press, Cambridge (2012)

    Book  Google Scholar 

  4. Khrennikov, A.: Ubiquitous Quantum Structure: From Psychology to Finance. Springer, Heidelberg (2010)

    Book  Google Scholar 

  5. Lawless, W.F., Bergman, M., Lou, J., Kriegel, N.N., Feltovich, N.: A quantum metric of organizational performance: terrorism and counterterrorism. Comput. Math. Organ. Theory 13, 241–281 (2007)

    Article  MATH  Google Scholar 

  6. Widdows, D.: Geometry and Meaning. CSLI Publications, Stanford (2004)

    MATH  Google Scholar 

  7. Aerts, D., Aerts, S., Broekaert, J., Gabora, L.: The violation of bell inequalities in the macroworld. Found. Phys. 30, 1387–1414 (2000)

    Article  MathSciNet  Google Scholar 

  8. Aerts, D., Aerts, S., Gabora, L.: Experimental evidence for quantum structure in cognition. In: Bruza, P., Sofge, D., Lawless, W., van Rijsbergen, K., Klusch, M. (eds.) QI 2009. LNCS, vol. 5494, pp. 59–70. Springer, Heidelberg (2009)

    Google Scholar 

  9. Galea, D., Bruza, P., Kitto, K., Nelson, D., McEvoy, C.: Modelling the acitivation of words in human memory: the spreading activation, spooky-activation-at-a-distance and the entanglement models compared. In: Song, D., Melucci, M., Frommholz, I., Zhang, P., Wang, L., Arafat, S. (eds.) QI 2011. LNCS, vol. 7052, pp. 149–160. Springer, Heidelberg (2011)

    Google Scholar 

  10. Arafat, S.: Senses in which quantum theory is an analogy for information retrieval. In: [38]

    Google Scholar 

  11. Cohen, T., Widdows, D.: Empirical distributional semantics: methods and biomedical applications. J. Biomed. Inform. 42(2), 390–405 (2009)

    Article  Google Scholar 

  12. Blei, D.M.: Probabilistic topic models. Commun. ACM 55, 77–84 (2012)

    Article  Google Scholar 

  13. Bohm, D.: Wholeness and the Implicate Order. Routledge Classics, republished 2002, Routledge, 1980

    Google Scholar 

  14. Widdows, D., Bruza, P.: Quantum information dynamics and open world science. In: Proceedings of the First International Symposium on Quantum Interaction, Stanford, California (2007)

    Google Scholar 

  15. Bratman, M.E.: Intention, Plans, and Practical Reason. Harvard University Press, Cambridge (1999)

    Google Scholar 

  16. Georgeff, M., Pell, B., Pollack, M., Tambe, M., Wooldridge, M.: The belief-desire-intention model of agency. In: Papadimitriou, C., Singh, M.P., Müller, J. (eds.) ATAL 1998. LNCS (LNAI), vol. 1555, pp. 1–10. Springer, Heidelberg (1999)

    Google Scholar 

  17. Kanerva, P.: Hyperdimensional computing: an introduction to computing in distributed representation with high-dimensional random vectors. Cogn. Comput. 1(2), 139–159 (2009)

    Article  Google Scholar 

  18. Bruza, P.D., Widdows, D., Woods, J.: A quantum logic of down below. In: Engesser, K., Gabbay, D., Lehmann, D. (eds.) Handbook of Quantum Logic and Quantum Structures: Quantum Logic, pp. 625–660. Elsevier, Amsterdam (2009)

    Chapter  Google Scholar 

  19. Trut, L.: Early canid domestication: the farm-fox experiment foxes bred for tamability in a 40-year experiment exhibit remarkable transformations that suggest an interplay between behavioral genetics and development. Am. Sci. 87(2), 160–169 (1999)

    Article  Google Scholar 

  20. Aerts, S., Kitto, K., Sitbon, L.: Similarity metrics within a point of view. In: [38]

    Google Scholar 

  21. Gärdenfors, P.: Conceptual Spaces: The Geometry of Thought. Bradford Books, MIT Press, Cambridge/London (2000)

    Google Scholar 

  22. Descartes, R.: The Geometry of René Descartes. Dover, New York (1637). Dover edn., with facsimile of the original

    Google Scholar 

  23. Grassmann, H.: Extension Theory. History of Mathematics Sources, American Mathematical Society, London Mathematical Society (1862). Translated by L.C. Kannenberg (2000)

    Google Scholar 

  24. Baeza-Yates, R., Ribiero-Neto, B.: Modern Information Retrieval. Addison Wesley/ACM Press, New York (1999)

    Google Scholar 

  25. Hastie, T., Tibshirani, R., Friedman, J.H.: The Elements of Statistical Learning. Springer Series in Statistics. Springer New York Inc., New York (2001)

    Book  MATH  Google Scholar 

  26. Mitchell, T.: Machine Learning. McGraw-Hill, Boston (1997)

    MATH  Google Scholar 

  27. Quine, W.V.O.: Word and object. MIT Press (MA), 2013 (orig. 1960)

    Google Scholar 

  28. Gabbay, D., Woods, J.: The new logic. Logic J. IGPL 9(2), 141–174 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  29. Widdows, D., Higgins, M.: Geometric ordering of concepts, logical disjunction, learning by induction, and spatial indexing. In: Compositional Connectionism in Cognitive Science, Washington, DC. AAAI Fall Symposium Series, October 2004

    Google Scholar 

  30. Boole, G.: An Investigation of the Laws of Thought. Macmillan, London (1854). Dover edn., 1958

    Google Scholar 

  31. Birkhoff, G., von Neumann, J.: The logic of quantum mechanics. Ann. Math. 37, 823–843 (1936)

    Article  Google Scholar 

  32. Varadarajan, V.S.: Geometry of Quantum Theory. Springer, Berlin (1985)

    MATH  Google Scholar 

  33. Busemeyer, J.R., Pothos, E.M., Franco, R., Trueblood, J.S.: A quantum theoretical explanation for probability judgment errors. Psychol. Rev. 118(2), 193 (2011)

    Article  Google Scholar 

  34. Kitto, K., Boschetti, F.: The quantum inspired modelling of changing attitudes and self-organising societies. In: [37]

    Google Scholar 

  35. Zorn, C., Smith, C.E.: Pseudo-classical non-separability and mass politics in two-party systems. In: [38]

    Google Scholar 

  36. Lawless, W.F., Sofge, D.A.: Social-psychological harmonic oscillators in the self-regulation of organizations and systems. In: [37]

    Google Scholar 

  37. Busemeyer, J.R., Dubois, F., Lambert-Mogiliansky, A., Melucci, M. (eds.): QI 2012. LNCS, vol. 7620. Springer, Heidelberg (2012)

    MATH  Google Scholar 

  38. Song, D., Melucci, M., Frommholz, I., Zhang, P., Wang, L., Arafat, S. (eds.): QI 2011. LNCS, vol. 7052. Springer, Heidelberg (2011)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Microsoft Bing, Bellevue, WA, USA

    Dominic Widdows

Authors
  1. Dominic Widdows
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dominic Widdows .

Editor information

Editors and Affiliations

  1. ETH Zurich, Zurich, Switzerland

    Harald Atmanspacher

  2. School of Management, University of Leicester, Leicester, United Kingdom

    Emmanuel Haven

  3. Queensland University of Technology, Brisbane, Queensland, Australia

    Kirsty Kitto

  4. Department of Physics and Astronomy Centre for Interdisciplinary Science, University of Leicester, Leicester, United Kingdom

    Derek Raine

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Widdows, D. (2014). Purposeful Choice and Point-of-View. In: Atmanspacher, H., Haven, E., Kitto, K., Raine, D. (eds) Quantum Interaction. QI 2013. Lecture Notes in Computer Science(), vol 8369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54943-4_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-54943-4_22

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54942-7

  • Online ISBN: 978-3-642-54943-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation