Skip to main content
SpringerLink
Log in

An Elementary Construction for a Non-elementary Procedure

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

We consider the problem of the product finite model property for binary products of modal logics. First we give a new proof for the product finite model property of the logic of products of Kripke frames, a result due to Shehtman. Then we modify the proof to obtain the same result for logics of products of Kripke frames satisfying any combination of seriality, reflexivity and symmetry. We do not consider the transitivity condition in isolation because it leads to infinity axioms when taking products.

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, Cambridge University Press, 2001.

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

  3. Gabbay, D., and V. Shehtman, 'Products of modal logics, part 1', Logic Journal of the IGPL 6:73-146, 1998.

    Google Scholar 

  4. Gabbay, D., and V. Shehtman, 'Products of modal logics, part 2', Logic Journal of the IGPL 8:165-210, 2000.

    Google Scholar 

  5. Gabbay, D., A. Kurucz, F. Wolter, and M. Zakharyaschev, Many-Dimensional Modal Logics: Theory and Applications, Studies in Logic, Elsevier, to appear.

  6. GrÄdel, E., P. Kolaitis, and M. Vardi, 'On the decision problem for two-variable first order logic', Bulletin of Symbolic Logic 3:53-69, 1997.

    Google Scholar 

  7. Marx, M., 'Complexity of products of modal logics', Journal of Logic and Computation 9:221-238, 1999.

    Google Scholar 

  8. Marx, M., and Sz. MikulÁs, 'Decidability of cylindric set algebras of dimension two and first-order logic with two variables', Journal of Symbolic Logic 64:1563-1572, 1999.

    Google Scholar 

  9. Marx, M., and Sz. MikulÁs, 'Products, or how to create modal logics of high complexity', Logic Journal of the IGPL 9:77-88, 2001.

    Google Scholar 

  10. Reynolds, M., 'A decidable logic of parallelism', Notre Dame Journal of Formal Logic 38:419-436, 1997.

    Google Scholar 

  11. Reynolds, M., and M. Zakharyaschev, 'On the products of linear modal logics', Journal of Logic and Computation 11(6): 909-931, December 2001.

    Google Scholar 

  12. Scott, D., 'A decision method for validity of sentences in two variables', Journal of Symbolic Logic 27:477, 1962.

    Google Scholar 

  13. Segerberg, K., 'Two-dimensional modal logic', Journal of Philosophical Logic 2:77-96, 1973.

    Google Scholar 

  14. Wolter, F., 'The product of converse PDL and polymodal K', Journal of Logic and Computation 10:223-251, 2000.

    Google Scholar 

  15. Wolter, F., and M. Zakharyaschev, 'Satisfiability problem in description logics with modal operators', In Proceedings of KR-98 (eds.: A.G. Cohn, L. Schubert, S.C. Shapiro), Morgan Kaufman, 1998, pp. 512-523.

  16. Wolter, F., and M. Zakharyaschev, 'Modal description logics: modalizing roles', Fundamenta Informaticae 39:411-438, 1999.

    Google Scholar 

  17. Wolter, F., and M. Zakharyaschev, 'Spatio-temporal representation and reasoning based on RCC-8', In Proceedings of KR-2000, Morgan Kaufman, 2000, pp. 3-14.

Download references

Author information

Authors and Affiliations

  1. Language and Inference Technology Group, ILLC, Universiteit van Amsterdam, Nieuwe Achtergracht 166, 1018 WV, Amsterdam, The Netherlands

    Maarten Marx

  2. School of Computer Science and Information Systems, Birkbeck College, University of London, Malet Street, London, WC1E 7HX, UK

    Szabolcs Mikulás

Authors
  1. Maarten Marx
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Szabolcs Mikulás
    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

Marx, M., Mikulás, S. An Elementary Construction for a Non-elementary Procedure. Studia Logica 72, 253–263 (2002). https://doi.org/10.1023/A:1021312628326

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1021312628326

Search

Navigation