Skip to main content
SpringerLink
Log in

On Independent Axiomatizability of Quasi-Normal Modal Logics

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

We give a negative solution to the problem, posed by A. Chagrov and M. Zakharyaschev, of whether every quasi-normal propositional modal logic can be axiomatized by an independent set of axioms, with the inference rules of Substitution and Modus Ponens.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Blackburn, P., M. de Rijke, and Y. Venema, Modal Logic, vol. 53 of Cambridge Tracts in Theoretical Computer Science, Cambridge University Press, 2001.

  2. Boolos,  G.S., The Logic of Provability, Cambridge University Press, 1993.

  3. Chagrov, A., and M. Zakharyaschev, On the independent axiomatizability of modal and intermediate logics, Journal of Logic and Computation, 5(3):287–302, 1995.

    Article  Google Scholar 

  4. Chagrov, A., and M. Zakharyaschev, Modal Logic, vol. 35 of Oxford Logic Guides, Oxford University Press, 1997.

  5. Citkin, A., Logic Notebook, Institute of Mathematics, Novesibirsk, 1986. In Russian.

  6. Kleiman, Y., Some questions in the theory of varieties of groups, Mathematics of the USSR–Izvestiya, 22(1): 33–66, 1984.

    Article  Google Scholar 

  7. Segerberg, K., An Essay in Classical Modal Logic, Upsalla, 1971.

  8. Solovay, R. M., Provability interpretations of modal logic, Israel Journal of Mathematics, 25: 287–304, 1976.

    Article  Google Scholar 

  9. Ten Cate, B., and T. Litak, The importance of being discrete, Technical Report, Institute for Logic, Language and Computation, University of Amsterdam, 2007.

Download references

Acknowledgements

We are grateful to the late Alexander Chagrov for stimulating the work presented here and to Marcus Kracht, Michael Zakharyaschev, and Mikhail Rybakov for discussions of ideas related to this work. We are indebted to anonymous reviewers for helping to improve the paper. The work on this paper has been supported by Russian Science Foundation, project 21-18-00195.

Author information

Authors and Affiliations

  1. Department of Mathematics, Tver State University, 33 Zhelyabova str., Tver, Russia

    Igor Gorbunov

  2. School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, WITS 2050, South Africa

    Dmitry Shkatov

Authors
  1. Igor Gorbunov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dmitry Shkatov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dmitry Shkatov.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Presented by Yde Venema.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gorbunov, I., Shkatov, D. On Independent Axiomatizability of Quasi-Normal Modal Logics. Stud Logica 110, 1189–1217 (2022). https://doi.org/10.1007/s11225-022-09992-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-022-09992-3

Keywords

Search

Navigation