Journal of Philosophical Logic

, Volume 32, Issue 5, pp 549–563 | Cite as

Extended Quantum Logic

  • Kenji Tokuo


The concept of quantum logic is extended so that it covers a more general set of propositions that involve non-trivial probabilities. This structure is shown to be embedded into a multi-modal framework, which has desirable logical properties such as an axiomatization, the finite model property and decidability.

Kripke semantics modal logic quantum logic 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dalla Chiara, M. L.: Quantum logic, in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, Vol. III, Reidel, Dordrecht, 1986, pp. 427–469.Google Scholar
  2. 2.
    Dubois, D., Esteva, F., Garcia, P., Godo, L. and Prade, H.: Similarity-based consequence relations, in C. Froidevaux and J. Kohlas (eds.), Symbolic and Quantitative Approaches to Reasoning and Uncertainty, Lecture Notes in Comput. Sci. 946, Springer, Berlin, 1995, pp. 171–179.Google Scholar
  3. 3.
    Fitting, M.: Many-valued modal logics, Fund. Inform. 15 (1991), 235–254.Google Scholar
  4. 4.
    Fitting, M.: Many-valued modal logics II, Fund. Inform. 17 (1992), 55–73.Google Scholar
  5. 5.
    Goldblatt, R. H.: Semantic analysis of orthologic, J. Philos. Logic 3 (1974), 19–35.Google Scholar
  6. 6.
    Hughes, G. E. and Cresswell, M. J.: A New Introduction to Modal Logic, Routledge, 1996.Google Scholar
  7. 7.
    Plaza, E., Esteva, F., Garcia, P., Godo, L. and Lopez de Mantaras, R.: A logical approach to case-based reasoning using fuzzy similarity relations, J. Inform. Sci. 106 (1998), 105–122.Google Scholar
  8. 8.
    Redei, M.: Quantum Logic in Algebraic Approach, Kluwer Academic Publishers, Dordrecht, 1998.Google Scholar
  9. 9.
    Rodriguez, R.: A modal account of similarity-based reasoning, Internat. J. Approx. Reason. 16 (1997), 235–260.Google Scholar
  10. 10.
    von Neumann, J., English translation by Beyer, R. T.: Mathematical Foundations of Quantum Mechanics, Princeton University Press, 1996.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Kenji Tokuo
    • 1
  1. 1.Graduate School of Human and Environmental StudiesKyoto UniversityKyotoJapan

Personalised recommendations