Advertisement

Logics of Linear Frames

  • Andrzej IndrzejczakEmail author
Chapter
Part of the Trends in Logic book series (TREN, volume 30)

Abstract

Logics of linear frames, called here for short linear logics form a particularly interesting and important class, especially in temporal interpretation. But we devote a separate Chapter for their treatment not because of their importance but rather because of special problems generated by their formalization in the setting of labelled systems.

Keywords

Modal Logic Temporal Logic Accessibility Relation Linear Temporal Logic Linear Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Reference

  1. [18]
    Baldoni, M. 1998. Normal multimodal logics: Automatic deduction and logic programming extension PhD thesis, Torino.Google Scholar
  2. [288]
    Zeman, J.J. 1973. Modal logic. Oxford: Oxford University Press.Google Scholar
  3. [63]
    Castellini, C. and A. Smaill. 2000. A systematic presentation of quantified modal logics. Logic Journal of the IGPL 10: 571–599.CrossRefGoogle Scholar
  4. [47]
    Bolotov, A., A. Basukoski, O. Grigoriev, and V. Shangin. 2006. Natural deduction calculus for linear-time temporal logic. Proceedings of jelia 2006. LNAI, Springer 4160.Google Scholar
  5. [118]
    Goubault-Larrecq J., and P.H. Schmitt. 1997. A tableau system for linear temporal logic. Proceedings of TACAS’97, 130–144, Springer.Google Scholar
  6. [183]
    Marx, M., S. Mikulas, and M. Reynolds. 2000. The mosaic method for temporal logics. In Automated reasoning with analytic tableaux and related methods, ed. R. Dyckhoff, Proc. of International Conference TABLEAUX 2000, Saint Andrews, Scotland, LNAI 1847, 324–340. New York: Springer.Google Scholar
  7. [116]
    Goré, R. 1992. Cut-free sequent and tableau systems for propositional normal modal logics, PhD thesis, University of Cambridge.Google Scholar
  8. [60]
    Burgess, J.P. 1984. Basic tense logic. In Handbook of philosophical logic, eds. D. Gabbay, and F. Guenthner, vol II, 89–133. Dordrecht: Reidel Publishing Company.Google Scholar
  9. [161]
    Kashima, R. 1994. Cut-free sequent calculi for some tense logics. Studia Logica 53: 119–135.CrossRefGoogle Scholar
  10. [281]
    Wansing, H. 2002. Sequent systems for modal logics. In Handbook of philosophical logic, eds. D. Gabbay, and F. Guenthner, vol IV, 89–133. Dordrecht: Reidel Publishing Company.Google Scholar
  11. [231]
    Rescher, N., and A. Urquhart. 1971. Temporal logic. New York: Springer-Verlag.Google Scholar
  12. [151]
    Indrzejczak, A. 2003. A labelled natural deduction system for linear temporal logic. Studia Logica 75(3): 345–376.CrossRefGoogle Scholar
  13. [88]
    Fisher, M., C. Dixon, and M. Peim. 2001. Clausal temporal resolution. ACM Transactions on Computational Logic 1(4).Google Scholar
  14. [149]
    Indrzejczak, A. 2002. Labelled analytic tableaux for S4.3. Bulletin of the Section of Logic 31(1): 15–26.Google Scholar
  15. [146]
    Indrzejczak, A. 2000. Multiple sequent calculus for tense logics. Abstracts of AiML and ICTL 2000: 93–104, Leipzig.Google Scholar
  16. [280]
    Wansing, H. 1998. Displaying modal logics. Dordrecht: Kluwer Academic Publishers.Google Scholar
  17. [284]
    Wolper, P. 1985. The tableau method for temporal logic: An overview. Logique et Analyse 28(110/111): 119–136.Google Scholar
  18. [140]
    Indrzejczak, A. 1994. Natural deduction system for tense logics. Bulletin of the Section of Logic 23(4): 173–179.Google Scholar
  19. [177]
    Lichtenstein, O., and A. Pnueli. 2000. Propositional temporal logics: Decidability and completeness. Logic Journal of the IGPL 8(1): 55–85.CrossRefGoogle Scholar
  20. [64]
    Catach, L. 1991. TABLEAUX: A general theorem prover for modal logics. Journal of Automated Reasoning 7(4): 489–510, 1991.CrossRefGoogle Scholar
  21. [252]
    Shimura, T. 1991. Cut-free systems for the modal logic S4.3 and S4.3GRZ. Reports on Mathematical Logic 25: 57–73.Google Scholar
  22. [112]
    Goldblatt, R.I. 1987. Logics of time and computation. Stanford: CSLI Lecture Notes.Google Scholar
  23. [104]
    Garson, J.W. 2005. Unifying quantified modal logic. Journal of Philosophical Logic 34: 621–649.CrossRefGoogle Scholar
  24. [194]
    Negri, S. 2005. Proof analysis in modal logic. Journal of Philosophical Logic 34: 507–544.CrossRefGoogle Scholar
  25. [175]
    Leszczyńska, D. 2008. The method of Socratic proofs for modal propositional logics: K5, S4.2, S4.3, S4M, S4F, S4R anf G. Studia Logica 89(3): 365–399.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Dept. LogicUniversity of LódzLódzPoland

Personalised recommendations