Skip to main content
SpringerLink
Log in

Analytic Tableau Systems and Interpolation for the Modal Logics KB, KDB, K5, KD5

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

We give complete sequent-like tableau systems for the modal logics KB, KDB, K5, and KD5. Analytic cut rules are used to obtain the completeness. Our systems have the analytic superformula property and can thus give a decision procedure. Using the systems, we prove the Craig interpolation lemma for the mentioned logics.

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

  2. Craig, W., 1957, 'Linear reasoning. A new form of the Herbrand-Gentzen theorem', pp. 250-268. Three uses of the Hebrand-Gentzen theorem in relating model theory to proof theory, pp. 269-285', Journal of Symbolic Logic 22.

    Google Scholar 

  3. Fitting, M., 1983, Proof Methods for Modal and Intuitionistic Logics, volume 169 of Synthese Library, D. Reidel, Dordrecht, Holland.

    Google Scholar 

  4. Gabbay, D.: 1972, 'Craig's interpolation theorem for modal logics', in: Conference in Mathematical Logic — London'70, Lecture Notes in Mathematics vol 255, pp. 111-127.

    Google Scholar 

  5. GorÉ, R.: 1999, 'Tableau methods for modal and temporal logics', in: D'Agostino, Gabbay, Hähnle, Posegga (eds.), Handbook of Tableau Methods, Kluwer Academic Publishers, pp. 297-396.

  6. Hintikka, K., 1955, 'Form and content in quantification theory', Acta Philosophica Fennica 8, 3-55.

    Google Scholar 

  7. Hudelmaier, J., 1996, 'Improved decision procedures for the modal logics K, T, S4', in: H. Kleine Büuning, editor, Proceedings of CSL'95, LNCS 1092, pp. 320-334.

  8. Hughes, G. and M. Cresswell, 1968, An Introduction to Modal Logic, Methuen.

  9. Kripke, S., 1963, 'Semantical analysis of modal logic, I. Normal modal propositional calculus', Z. Math. Logic Grundlag 9, 67-96.

    Google Scholar 

  10. Maksimova, L., 1991, 'Amalgamation and interpolation in normal modal logics', Studia Logica 50, 458-471.

    Google Scholar 

  11. Massacci, F., 1994, 'Strongly analytic tableaux for normal modal logics', in: A. Bundy, editor, Proceedings of CADE-12, LNAI 814, pp. 723-737.

  12. Nguyen, L., 2000a, 'Clausal tableau systems and space bounds for the modal logics K, KD, T, KB, KDB, and B', Technical Report TR 00-01(261), Warsaw University.

  13. Nguyen, L., 2000b, 'Sequent-Like tableau systems with the analytic superformula property for the modal logics KB, KDB, K5, KD5', in: R. Dyckhoff, editor, Proceedings of TABLEAUX 2000, LNAI 1847, pp. 341-351.

  14. Rautenberg, W., 1983, 'Modal tableau calculi and interpolation', Journal of Philosophical Logic 12, 403-423.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Informatics, Warsaw University, ul. Banacha 2, 02-097, Warsaw, Poland

    Linh Anh Nguyen

Authors
  1. Linh Anh Nguyen
    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

Nguyen, L.A. Analytic Tableau Systems and Interpolation for the Modal Logics KB, KDB, K5, KD5. Studia Logica 69, 41–57 (2001). https://doi.org/10.1023/A:1013834410884

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1013834410884

Search

Navigation