Skip to main content
SpringerLink
Log in

Reasoning about Quantum Actions: A Logician’s Perspective

  • Chapter
  • First Online:
New Challenges to Philosophy of Science

Part of the book series: The Philosophy of Science in a European Perspective ((PSEP,volume 4))

  • 1800 Accesses

Abstract

In this paper I give an overview of how the work on quantum dynamic logic for single systems (as developed in [2]) builds on the concepts of (dynamic) modal logic and incorporates the methodology of logical dynamics and action based reasoning into its setting. I show in particular how one can start by modeling quantum actions (i.e. measurements and unitary evolutions) in a dynamic logic framework and obtain a setting that improves on the known theorems in traditional quantum logic (stated in the context of orthomodular lattices).

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 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover 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 setting can be extended with a classical negation, which then means that not all “sets of states” P ⊆ S will correspond to “quantum testable properties”. In [4, 5] we showed how this enriches the setting and gives us more expressive power than traditional Quantum Logic.

References

  1. Baltag A. and Smets S., 2004, “The Logic of Quantum Programs”, in: P. Selinger (Ed.) Proceedings of the 2nd International Workshop on Quantum Programming Languages (QPL2004), TUCS General Publication, 33, Turku Center for Computer Science, pp. 39-56.

    Google Scholar 

  2. Baltag A. and Smets S., 2005, “Complete Axiomatizations of Quantum Actions”, in: International Journal of Theoretical Physics, 44, 12, pp. 2267-2282.

    Google Scholar 

  3. Baltag A. and Smets S., 2006, “LQP: The Dynamic Logic of Quantum Information”, in: Mathematical Structures in Computer Science, Special Issue on Quantum Programming Languages, 16, 3, pp. 491-525.

    Google Scholar 

  4. Baltag A. and Smets S., 2008, “A Dynamic-Logical Perspective on Quantum Behavior”, in: L. Horsten and I. Douven (Eds.), Special Issue: Applied Logic in the Philosophy of Science, Studia Logica, 89, pp. 185-209.

    Google Scholar 

  5. Baltag A. and Smets S., 2011,. “Quantum Logic as a Dynamic Logic”, in: T. Kuipers, J. van Benthem and H. Visser (Eds.), Synthese, 179, 2, pp. 285-306.

    Google Scholar 

  6. Baltag A. and Smets S., 2011, “The Dynamic Turn in Quantum Logic”, in: Synthese, Online First at Springer.

    Google Scholar 

  7. van Benthem J., 1996, Exploring Logical Dynamics, Stanford, CA: CSLI Publications.

    Google Scholar 

  8. van Benthem J., 2011, Logical Dynamics of Information and Interaction, Cambridge: Cambridge University Press.

    Book  Google Scholar 

  9. Birkhoff G., and von Neumann J., 1936, “The Logic of Quantum Mechanics”, in: Annals of Mathematics, 37, pp. 823-843, reprinted in: C. A. Hooker (Ed.), 1975, The Logico-algebraic Approach to Quantum Mechanics, vol. 1, Dordrecht: D. Reidel Publishing Company, pp.1-26.

    Google Scholar 

  10. Blute R., Desharnais J., Edalat A. and Panangaden P., 1997, “Bisimulation for labelled Markov Processes”, in: Proceedings of the Twelfth IEEE Symposium on Logic in Computer Science, Warsaw, Poland.

    Google Scholar 

  11. Danos V., Desharnais J., Laviolette F., and Panangaden P., 2006, “Bisimulation and Cocongruence for Probabilistic Systems”, in: Information and Computation 204, 4, pp. 503-523.

    Google Scholar 

  12. Desharnais J., Gupta V., Jagadeesan R. and Panangaden P., 2003, “Approximating Labeled Markov Processes”, in: Information and Computation 184, 1, pp. 160-200.

    Google Scholar 

  13. Fokkink W., 2000, Introduction to Process Algebra. Germany: Springer.

    Book  Google Scholar 

  14. Goldblatt R., 1984, “Orthomodularity Is Not Elementary”, in: The Journal of Symbolic Logic 49, pp. 401-404.

    Google Scholar 

  15. Harel D., Kozen D. and Tiuryn J., 2000, Dynamic Logic. Cambridge (Mass.): The MIT Press.

    Google Scholar 

  16. Hartmann S., 1996, “The World as a Process: Simulations in the Natural and Social Sciences” in: R. Hegselmann et al. (Eds.), Modelling and Simulation in the Social Sciences from the Philosophy of Science Point of View, Theory and Decision Library, Dordrecht: Kluwer, pp. 77-100.

    Chapter  Google Scholar 

  17. Jacobs B., n.d., Introduction to Coalgebra. Towards Mathematics of States and Observations. Book in preparation, on-line at http://www.cs.ru.nl/~bart/PAPERS/index.html

  18. Jauch, J. M., 1968, Foundations of Quantum Mechanics, Addison-Wesley, Reading, Massachusetts.

    Google Scholar 

  19. Jauch, J. M. and Piron C., 1969, “On the Structure of Quantal Proposition Systems”, in: Helvetica Physica Acta 42, pp. 842-848.

    Google Scholar 

  20. Jauch, J. M., and Piron C., 1970, “What is ‘Quantum-Logic’?” in: P. G. O. Freund, C. J. Goebel, and Y. Nambu (Eds.) Quanta. Chicago: The University of Chicago Press.

    Google Scholar 

  21. Kalmbach G., 1983, Orthomodular Lattices. London–New York: Academic Press.

    Google Scholar 

  22. Kurtz A., 2000, Logics for Coalgebras and Applications to Computer Science, PhD-thesis, Mnchen, Germany.

    Google Scholar 

  23. Larsen K. G. and Skou A., 1991, “Bisimulation Through Probabilistic Testing”, in: Information and Computation 94, pp. 1-28.

    Google Scholar 

  24. Mayet R., 1998, “Some Characterizations of the Underlying Division Ring of a Hilbert Lattice by Automorphisms”, in: International Journal of Theoretical Physics 37, 1, pp. 109-114.

    Google Scholar 

  25. Moore D. J., 1999, “On State Spaces and Property Lattices”, in: Studies in History and Philosophy of Modern Physics 30, pp. 61-83.

    Google Scholar 

  26. Panangaden P., 2006, “Notes on Labelled Transition Systems and Bisimulation”, course-notes, October.

    Google Scholar 

  27. Piron C., 1964, Axiomatique quantique (PhD-Thesis), Helvetica Physica Acta, 37, pp. 439-468; English Translation by Cole M.: Quantum Axiomatics RB4 Technical memo 107/106/104, GPO Engineering Department, London.

    Google Scholar 

  28. Piron C., 1976, Foundations of Quantum Physics. W.A. Benjamin Inc., Massachusetts.

    Google Scholar 

  29. Piron C., 1990 Mécanique quantique. Bases et applications, Presses polytechniques et universitaires romandes, Lausanne (Second corrected ed. 1998).

    Google Scholar 

  30. Smets S., 2010, “Logic and Quantum Physics”, in: A. Gupta and J. van Benthem (Eds.), Journal of the Indian Council of Philosophical Research Special Issue XXVII, 2.

    Google Scholar 

  31. Solèr M. P., 1995, “Characterization of Hilbert Spaces by Orthomodular Spaces”, in: Communications in Algebra 23, 1, pp. 219-243.

    Google Scholar 

Download references

Acknowledgement

The research presented here has been made possible by VIDI grant 639.072.904 of the Netherlands Organization for Scientic Research (NWO).

Author information

Authors and Affiliations

  1. Institute for Logic, Language and Computation, University of Amsterdam, 94242, 1090 GE, Amsterdam, The Netherlands

    Sonja Smets

Authors
  1. Sonja Smets
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sonja Smets .

Editor information

Editors and Affiliations

  1. Aarhus University, Ny Munkegade 1520, Aarhus, 8000, Denmark

    Hanne Andersen

  2. Inst. History & Foundations of Science, Utrecht University, Budapestlaan 6, Utrecht, 3584 CD, Netherlands

    Dennis Dieks

  3. , Faculty of Humanities, University of A Coruña, Dr. Vazquez Cabrera street, w/n, Ferrol, 15.403, Spain

    Wenceslao J. Gonzalez

  4. , Philosophy School of Social Science, University of Manchester, Manchester, M13 9PL, United Kingdom

    Thomas Uebel

  5. Centre Artificial Intelligence (CENTRA), Department of Computer Science, New University of Lisbon, Monte de Caparica, Lisbon, 2829-516, Portugal

    Gregory Wheeler

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Smets, S. (2013). Reasoning about Quantum Actions: A Logician’s Perspective. In: Andersen, H., Dieks, D., Gonzalez, W., Uebel, T., Wheeler, G. (eds) New Challenges to Philosophy of Science. The Philosophy of Science in a European Perspective, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5845-2_11

Download citation

Publish with us

Policies and ethics

Search

Navigation