Skip to main content
SpringerLink
Log in

A Predicative Characterization of Quantum States and Matte Blanco’s Bi-logic

  • 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

We show a correspondence between a predicative characterization of quantum states, we have recently introduced, and bi-logic, proposed by the Chilean psychoanalyst I. Matte Blanco. In bi-logic, the logic of the unconscious is characterized by “infinite” objects and by the “symmetric mode”, without negation and logical consequence. In the quantum model it is possible to define a class of first order domains, called virtual singletons, that are uncountable, and that allow a generalization of the notion of duality, called symmetry. Symmetry makes negation and logical consequence collapse, in favour of different links between judgements, that are due to quantum correlations.

Work partially supported by the ex-\(60\,\%\) funds of the University of Padova.

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.

    Notice that the premises in \(\varGamma \) do not depend on the variable \(z\), since the measurement hypothesis cannot depend on its eventual outcome.

References

  1. Aerts, D.: Quantum structure in cognition. J. Math. Psychol. 53, 314–348 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  2. Aerts, D., Broekaert, J., Gabora, L., Sozzo, S.: Quantum structure and human thought. Behav. Brain Sci. 36, 274–276 (2013)

    Article  Google Scholar 

  3. Aerts, D., Gabora, L., Sozzo, S.: Concepts and their dynamics: a quantum-theoretic modeling of human thought. Top. Cogn. Sci. ArXiv: 1206.1069 [cs.AI] (in print)

    Google Scholar 

  4. Aerts, D., Sozzo, S.: Quantum structure in cognition: why and how concepts are entangled. In: Song, D., Melucci, M., Frommholz, I., Zhang, P., Wang, L., Arafat, S. (eds.) QI 2011. LNCS, vol. 7052, pp. 116–127. Springer, Berlin (2011)

    Google Scholar 

  5. Aerts, D., Sozzo, S: Quantum entanglement in concept combinations. Submitted in Int. J. Theor. Phys. ArXiv:1302.3831 [cs.AI] (2013)

  6. Battilotti, G.: Interpreting quantum parallelism by sequents. Int. J. Theor. Phys. 49, 3022–3029 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  7. Battilotti, G.: Characterization of quantum states in predicative logic. Int. J. Theor. Phys. 50, 3669–3681 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  8. Battilotti, G.: Quantum states as virtual singletons: converting duality into symmetry. Int. J. Theor. Phys. arXiv 1304.2788[math.LO] (to appear)

    Google Scholar 

  9. Bruza, P.D., Lawless, W., van Rijsbergen, C.J., Sofge, D. (eds.): Proceedings of the AAAI Spring Symposium on Quantum Interaction, 27–29 March. Stanford University, Stanford (2007)

    Google Scholar 

  10. Bruza, P.D., Lawless, W., van Rijsbergen, C.J., Sofge, D. (eds.): Quantum Interaction: Proceedings of the Second Quantum Interaction Symposium. College Publications, London (2008)

    Google Scholar 

  11. Bruza, P.D., Sofge, D., Lawless, W., van Rijsbergen, K., Klusch, M. (eds.): QI 2009. LNCS (LNAI), vol. 5494. Springer, Heidelberg (2009)

    MATH  Google Scholar 

  12. Busemeyer, J.R., Pothos, E., Franco, R., Trueblood, J.S.: A quantum theoretical explanation for probability judgment ‘errors’. Psychol. Rev. 118, 193–218 (2011)

    Article  Google Scholar 

  13. Busemeyer, J.R., Bruza, P.D.: Quantum Models of Cognition and Decision. Cambridge University Press, Cambridge (2012)

    Book  Google Scholar 

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

    MATH  Google Scholar 

  15. Khrennikov, A.: Human subconscious as the p-adic dynamical system. J. Theor. Biol. 193, 179–196 (1998)

    Article  Google Scholar 

  16. Khrennikov, A.: Modelling of psychological behavior on the basis of ultrametric mental space: encoding of categories by balls. P-Adic Numbers Ultrametric Anal. Appl. 2(1), 1–20 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  17. Lauro-Grotto, R.: The unconscious as an ultrametric set. Am. Imago 64(4), 535–543 (2008)

    Article  Google Scholar 

  18. Maietti, M.E., Sambin, G.: Toward a minimalist foundation for constructive mathematics. In: Crosilla, L., Schuster, P. (eds.) From Sets and Types to Topology and Analysis: Towards Practicable Foundations for Constructive Mathematics. Oxford UP, Oxford (2005)

    Google Scholar 

  19. Matte Blanco, I.: The Unconscious as Infinite Sets. An Essay in Bi-Logic. Duckworth, London (1975)

    Google Scholar 

  20. Murtagh, F.: Ultrametric model of mind, I: Review. P-Adic Numbers Ultrametric Anal. Appl. 4(3), 193–206 (2012)

    Article  MathSciNet  Google Scholar 

  21. Sambin, G., Battilotti, G., Faggian, C.: Basic logic: reflection, symmetry, visibility. J. Symbolic Logic 65, 979–1013 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  22. 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

Acknowledgements

The present note has been written some years after the valuable suggestion by Stuart Hameroff, who proposed to compare quantum logics and Matte Blanco’s bi-logic. His suggestion became more and more significant to me with the development of the predicative model here considered.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Padova, Padova, Italy

    G. Battilotti

Authors
  1. G. Battilotti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. Battilotti .

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

Battilotti, G. (2014). A Predicative Characterization of Quantum States and Matte Blanco’s Bi-logic. 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_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-54943-4_16

  • 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