Skip to main content
Log in

A Modal Logic for Discretely Descending Chains of Sets

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

We present a modal logic for the class of subset spaces based on discretely descending chains of sets. Apart from the usual modalities for knowledge and effort the standard temporal connectives are included in the underlying language. Our main objective is to prove completeness of a corresponding axiomatization. Furthermore, we show that the system satisfies a certain finite model property and is decidable thus.

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

Access this article

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, Cambridge University Press, 200

  2. Chagrov, A., and M. Zakharyaschev, Modal Logic, Clarendon Press, 199

  3. Dabrowski, A., L. S. Moss, and R. Parikh, 'Topological Reasoning and The Logic of Knowledge', Annals of Pure and Applied Logic 78:73–110, 1996.

    Google Scholar 

  4. Fagin, R., J. Y. Halpern, Y. Moses, and M. Y. Vardi, Reasoning about Knowledge, MIT Press, 1995.

  5. Gabbay, D. M., A. Kurucz, F. Wolter, and M. Zakharyaschev, Many-dimensional Modal Logics: Theory and Applications, Elsevier, 2003.

  6. Georgatos, K., 'Knowledge on Treelike Spaces', Studia Logica 59:271–301, 1997.

    Google Scholar 

  7. Goldblatt, R., Logics of Time and Computation, Center for the Study of Language and Information, 1992.

  8. Halpern, J. Y., and Y. Moses, 'Knowledge and Common Knowledge in a Distributed Environment', Journal of the ACM 37:549–587, 1990.

    Google Scholar 

  9. Halpern, J. Y., R. van der Meyden, and M. Y. Vardi, 'Complete Axiomatizations for Reasoning about Knowledge and Time', SIAM Journal on Computing, to appear.

  10. Heinemann, B., Topological Nexttime Logic. In Advances in Modal Logic 1, 99–113, Kluwer, 1998.

  11. Heinemann, B., 'Temporal Aspects of the Modal Logic of Subset Spaces', Theoretical Computer Science 224:135–155, 1999.

    Google Scholar 

  12. Heinemann, B., About the Temporal Decrease of Sets, In Temporal Representation and Reasoning, 234–239, IEEE Computer Society Press, 2001.

  13. Heinemann, B., Axiomatizing Modal Theories of Subset Spaces (An Example of the Power of Hybrid Logic), In HyLo@LICS, Proceedings, 69–83, Copenhagen, 2002.

  14. Hintikka, J., Knowledge and Belief, Cornell University Press, 1977.

  15. Hodkinson, I., F. Wolter, and M. Zakharyaschev, 'Decidable Fragments of First-Order Temporal Logics', Annals of Pure and Applied Logic 106:85–134, 2000.

    Google Scholar 

  16. Meyer, J.-J. Ch., and W. van der Hoek, Epistemic Logic for AI and Computer Science, Cambridge University Press, 1995

  17. Sistla, A. P., and E. M. Clarke, 'The Complexity of Propositional Linear Temporal Logics', Journal of the ACM 32:733–749, 1985.

    Google Scholar 

  18. Weihrauch, K., Computable Analysis, Springer-Verlag, 2000.

  19. Weiss, M. A., and R. Parikh, 'Completeness of Certain Bimodal Logics for Subset Spaces', Studia Logica 71:1–30, 2002.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Heinemann, B. A Modal Logic for Discretely Descending Chains of Sets. Studia Logica 76, 67–90 (2004). https://doi.org/10.1023/B:STUD.0000027467.49608.9d

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:STUD.0000027467.49608.9d

Navigation