Skip to main content
SpringerLink
Log in

Models for stronger normal intuitionistic modal logics

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

This paper, a sequel to “Models for normal intuitionistic modal logics” by M. Božić and the author, which dealt with intuitionistic analogues of the modal system K, deals similarly with intuitionistic analogues of systems stronger than K, and, in particular, analogues of S4 and S5. For these prepositional logics Kripke-style models with two accessibility relations, one intuitionistic and the other modal, are given, and soundness and completeness are proved with respect to these models. It is shown how the holding of formulae characteristic for particular logics is equivalent to conditions for the relations of the models. Modalities in these logics are also investigated.

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. J. L. Bell and M. Machover, A Course in Mathematical Logic, North-Holland, Amsterdam, 1977.

    Google Scholar 

  2. G. Boolos, The Unprovability of Consistency: An Essay in Modal Logic, Cambridge University Press, Cambridge, 1979.

    Google Scholar 

  3. M. Božić and K. Došen, Models for normal intuitionistic modal logics, Studia Logica 43 (1984), pp. 15–43.

    Google Scholar 

  4. R. A. Bull, A modal extension of intuitionistic logic, Notre Dame Journal of Formal Logic 6 (1965), pp. 142–146.

    Google Scholar 

  5. R. A. Bull, MIPC as the formalization of an intuitionist concept of modality, The Journal of Symbolic Logic 31 (1966), pp. 609–616.

    Google Scholar 

  6. B. F. Chellas, Modal Logic: An Introduction, Cambridge University Press, Cambridge, 1980.

    Google Scholar 

  7. M. C. Fitting, Intuitionistic Logic Model Theory and Forcing, North-Holland, Amsterdam, 1969.

    Google Scholar 

  8. D. M. Gabbay, Semantical Investigations in Heyting's Intuitionistic Logic, Reidel, Dordrecht, 1981.

    Google Scholar 

  9. J. Hintikka, A closure and complement result for nested topologies, Fundamenta Mathematicae 57 (1965), pp. 97–106.

    Google Scholar 

  10. M. Mihajlova, Reduction of modalities in several intuitionistic modal logics, Comptes rendus de l'Académie bulgare des Sciences 33 (1980), pp. 743–745.

    Google Scholar 

  11. D. Prawitz, Natural Deduction: A Proof-Theoretical Study, Almqvist & Wiksell, Stockholm, 1965.

    Google Scholar 

  12. H. Rasiowa and R. Sikorski, The Mathematics of Metamathematics, Pańsfrwowe Wydawnictwo Naukowe, Warszawa, 1963.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Matematički Institut, Knez Mihailova 35, Belgrade, Yugoslavia

    Kosta Došen

Authors
  1. Kosta Došen
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This paper presents results of an investigation of intuitionistic modal logic conducted in collaboration with Dr Milan Božić.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Došen, K. Models for stronger normal intuitionistic modal logics. Stud Logica 44, 39–70 (1985). https://doi.org/10.1007/BF00370809

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00370809

Keywords

Search

Navigation