A labelled sequent system for tense logic Kt

  • Nicolette Bonnette
  • Rajeev Goré
Scientific Track
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1502)


The method of labelled tableaux for proof search in modal logics is extended and modified to give a labelled sequent system for the tense logic K t. Soundness and completeness proofs are sketched, and results of an initial lean Prolog implementation in the programming style of lean T A P are presented. The sequent system is modular in that small modifications capture any combination of the reflexive, transitive, euclidean, symmetric and serial extensions of K t.


automated deduction labelled deductive system lean deduction sequent system tense logic 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BG97]
    B Beckert and R Goré. Free variable tableaux for propositional modal logics. In Proc. TABLEAUX-97, LNCS 1227, pages 91–106. Springer, 1997.Google Scholar
  2. [BG98]
    N Bonnette and R Goré. A labelled sequent system for tense logic K t. Technical Report TR-ARP-1-1998, ARP, 1998. Scholar
  3. [BP95]
    B Beckert and J Posegga. leanT A P: Lean tableau-based deduction. Journal of Automated Reasoning, 15(3):339–358, 1995.MATHMathSciNetCrossRefGoogle Scholar
  4. [Fit83]
    M Fitting. Proof Methods for Modal and Intuitionistic Logics, volume 169 of Synthese Library. D. Reidel, Dordrecht, Holland, 1983.Google Scholar
  5. [Fit98]
    M Fitting. Leantap revisited. J. of Logic and Computation 8:33–47, 1998.MATHMathSciNetCrossRefGoogle Scholar
  6. [Gab96]
    D Gabbay. Labelled Deductive Systems. Oxford University Press, 1996.Google Scholar
  7. [Gor95]
    R Goré. Tableau methods for modal and temporal logics. Technical Report TR-ARP-15-1995, ANU, 1995.Google Scholar
  8. [Gov95]
    G Governatori. Labelled tableaux for multi-modal logics. In Proc. TABLEAUX-95, LNCS 918, pages 79–94. Springer, 1995.Google Scholar
  9. [HC84]
    G E Hughes and M J Cresswell. A Companion to Modal Logic. Methuen, London, 1984.MATHGoogle Scholar
  10. [HC96]
    G E Hughes and M J Cresswell. A New Introduction To Modal Logic. Routledge, 1996.Google Scholar
  11. [HS96]
    A Heuerding and S Schwendimann. On the modal logic K plus theories. In Proc. CSL95, volume LNCS 1092, pages, 308–319. Springer, 1996.Google Scholar
  12. [HS98]
    U. Hustadt and R. A. Schmidt. Simplification and backjumping in modal tableau. In Proc. TABLEAUX-98, LNAI 1397, pages 189–201. Springer, 1998.Google Scholar
  13. [HSZ96]
    A Heuerding, M Seyfried, and H Zimmermann. Efficient loop-check for backward proof search in some non-classical logics. In Proc. TABLEAUX-96, LNAI 1071, pages 210–225. Springer, 1996.Google Scholar
  14. [Kan57]
    S. Kanger. Provability in Logic. Stockholm Studies in Philosophy, University of Stockholm, Almqvist and Wiksell, Sweden, 1957.Google Scholar
  15. [Mas94]
    F Massacci. Strongly analytic tableaux for normal modal logics. In A Bundy, editor, Proc. CADE-12, LNAI 814, pages 723–737. Springer, 1994.Google Scholar
  16. [Mas98]
    F Massacci. Simplification: a general constraint propagation technique for propositional and modal tableaux. In Proc. TABLEAUX-98, LNAI 1397, pages 217–231. Springer, 1998.Google Scholar
  17. [NFKT87]
    H Nakamura, M Fujita, S Kono, and H Tanaka. Temporal logic based fast verification system using cover expressions. In C H Séquin, editor, Proceedings VLSI’87, pages 101–111, 1987.Google Scholar
  18. [PC96]
    J Pitt and J Cunningham. Distributed modal theorem proving with KE. In Proc. TABLEAUX-96, LNAI 1071, pages 160–176. Springer, 1996.Google Scholar
  19. [RU71]
    N Rescher and A Urquhart. Temporal Logic. Springer-Verlag, 1971.Google Scholar
  20. [Sti96]
    C Stirling. Modal and temporal logics for processes. Lecture Notes in Computer Science, 1043:149–237, 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Nicolette Bonnette
    • 1
  • Rajeev Goré
    • 2
  1. 1.Automated Reasoning ProjectAustralian National UniversityCanberra
  2. 2.Department of Computer ScienceAustralian National UniversityCanberra

Personalised recommendations