Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Duality between modal algebras and neighbourhood frames

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

This paper presents duality results between categories of neighbourhood frames for modal logic and categories of modal algebras (i.e. Boolean algebras with an additional unary operation). These results extend results of Goldblatt and Thomason about categories of relational frames for modal logic.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

    Google Scholar 

  2. L. L. Esakia,On topological Kripke models (in Russian),Doklady Akademii Nauk SSSR 214 (1974), pp. 298–301.

    Google Scholar 

  3. L. L. Esakia,Heyting Algebras I: Duality Theory (in Russian), Metsniereba, Tbilisi, 1985.

    Google Scholar 

  4. R. I. Goldblatt,Metamathematics of modal logic,Reports on Mathematical Logic 6 (1976), pp. 41–77; 7 (1976), pp. 21–52 (all page references in the text are to the first part, in 6 (1976)).

    Google Scholar 

  5. G. Hansoul,A duality for Boolean algebras with operators,Algebra Universalis 17 (1983), pp. 34–49.

    Article  Google Scholar 

  6. B. Jónsson andA. Tarski,Boolean algebras with operators: Part I,American Journal of Mathematics 73 (1951), pp. 891–939.

    Article  Google Scholar 

  7. B. Pareigis,Categories and Functors, Academic Press, New York, 1970.

    Google Scholar 

  8. R. S. Pierce,Compact Zero-Dimensional Metric Spaces of Finite Type, Memoirs of the American Mathematical Society 130 (1972).

  9. H. Rasiowa andR. Sikorski The Mathematics of Metamathematics, Państwowe Wydawnictwo Naukowe, Warsaw, 1963.

    Google Scholar 

  10. K. Segerberg,An Essay in Classical Modal Logic, University of Uppsala, Uppsala, 1971.

    Google Scholar 

  11. S. K. Thomason,Categories of frames for modal logic,The Journal of Symbolic Logic 40 (1975), pp. 439–442.

    Article  Google Scholar 

  12. J. Williams,Structure diagrams for primitive Boolean algebras,Proceedings of the American Mathematical Society 47 (1975), pp. 1–9.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Matematički Institut, Knez Mihailova 35, P.F. 367, 11001, Beograd, Yugoslavia

    Kosta Došen

Authors
  1. Kosta Došen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Došen, K. Duality between modal algebras and neighbourhood frames. Stud Logica 48, 219–234 (1989). https://doi.org/10.1007/BF02770513

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02770513

Keywords

Search

Navigation