Studia Logica

, Volume 103, Issue 5, pp 985–1003 | Cite as

Hilbert-Style Axiom Systems for the Matrix-Based Logics RMQ and RMQ *

  • Albert J. J. AnglbergerEmail author
  • Jonathan Lukic


This paper deals with the axiomatizability problem for the matrix-based logics RMQ and RMQ *. We present a Hilbert-style axiom system for RMQ , and a quasi-axiomatization based on it for RMQ *. We further compare these logics to different well-known modal logics, and assess its status as relevance logics.


Many-valued logic Relevance logic Quantum Logic RMQ 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Anderson A. R., Belnap N.D.: Entailment: The Logic of Relevance and Necessity. Princeton University Press, Princeton (1975)Google Scholar
  2. 2.
    Ballarin, R., Modern origins of modal logic, in E. N. Zalta, (ed.), The Stanford Encyclopedia of Philosophy. Winter 2010 edition, 2010.Google Scholar
  3. 3.
    Czermak, J., Eine endliche axiomatisierung von SS1M, in E. Morscher, O. Neumaier, and G. Zecha, (eds.), Philosophie als Wissenschaft—Essays in Scientific Philosophy, Comes Verlag, Bad Reichenhall, 1981, pp. 245–257.Google Scholar
  4. 4.
    Gottwald S.: A Treatise on Many-Valued Logic. Research Studies Press, Taunton (2000)Google Scholar
  5. 5.
    Hughes, G. E., and M. J. Cresswell, A New Introduction to Modal Logic. Routledge, 1996.Google Scholar
  6. 6.
    Rosser J. B., Turquette A. R.: Axiom schemes for M-valued propositional calculi. The Journal of Symbolic Logic 10(3), 61–82 (1945)CrossRefGoogle Scholar
  7. 7.
    Rosser J. B., Turquette A. R.: Many-Valued Logics. North-Holland Publishing, Amsterdam (1952)Google Scholar
  8. 8.
    Weingartner P.: Matrix-based logics for applications in physics. Review of Symbolic Logic 2, 132–163 (2009)CrossRefGoogle Scholar
  9. 9.
    Weingartner P.: An alternative propositional calculus for application to empirical sciences. Studia Logica 95, 233–257 (2010)CrossRefGoogle Scholar
  10. 10.
    Weingartner P.: Basis logic for application in physics and its intuitionistic alternative. Foundations of Physics 40(9–10), 1578–1596 (2010)CrossRefGoogle Scholar
  11. 11.
    Yonemitsu, N., A note on the modal systems, von Wright’s and Lewis’s S1, Memoirs of the Osaka University of the Liberal Arts and Education Bulletin of Natural Science 45(4), 1955.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.MCMPLMU MunichMunichGermany
  2. 2.University of SalzburgSalzburgAustria

Personalised recommendations