Sharpening the Undecidability of Interval Temporal Logic

  • Kamal Lodaya
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1961)


Interval temporal logics (ITLs) were introduced in the philosophy of time (see [Ben95] for a survey) but have proved useful in artificial intelligence and computer science [All83, HMM83, HS91, ZHR91]. They provide a rich specification language for systems working with dense time (for example, [RRM93]). By now, there is a whole menagerie of ITLs. In this paper, we work with the simplest (propositional) ITLs and discuss their decidability.


Modal Logic Turing Machine Dense Time Tense Logic Propositional Modal 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [All83]
    J. F. Allen. Maintaining knowledge about temporal intervals, Commun. ACM 26,11 (Nov 1983) 832–843.zbMATHCrossRefGoogle Scholar
  2. [Ben95]
    J. van Benthem. Temporal logic, in D. M. Gabbay, C. Hogger and J. A. Robinson (eds), Handbook of logic in artificial intelligence and logic programming IV (Oxford, 1995) 241–350.Google Scholar
  3. [Bur82]
    J. P. Burgess. Axioms for tense logic II: time periods, Notre Dame J. FL 23,4 (Oct 1982) 375–383.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [Dut95]
    B. Dutertre. On first order interval temporal logic, Tech Report, Royal Holloway College, University of London (1995), [Also in Proc. 10th LICS (1995).]
  5. [HMM83]
    J. Y. Halpern, Z. Manna and B. Moszkowski. A hardware semantics based on temporal intervals, Proc. ICALP, LNCS 154 (1983) 278–291.Google Scholar
  6. [HS91]
    J. Y. Halpern and Y. Shoham. A propositional modal logic of time intervals, J. ACM 38,4 (Oct 1991) 935–962.zbMATHCrossRefMathSciNetGoogle Scholar
  7. [LR00]
    K. Lodaya and S. Roy. Lines, a while and intervals, presented at the Workshop on Many-dimensional logical systems, ESSLLI’ 00, Birmingham (2000).Google Scholar
  8. [Pan95]
    P. K. Pandya. Some extensions to propositional meanvalue calculus: expressiveness and decidability, Proc. CSL, LNCS 1092 (1995) 434–451.Google Scholar
  9. [Rab98]
    A. Rabinovich. On the decidability of continuous time specification formalisms, J. Logic Comput. 8,5 (1998) 669–678.zbMATHCrossRefMathSciNetGoogle Scholar
  10. [RP86]
    R. Rosner and A. Pnueli. A choppy logic, Proc. 1st LICS (1986) 306–313.Google Scholar
  11. [RRM93]
    A. P. Ravn, H. Rischel and K. M. Hansen. Specifying and verifying requirements of real-time systems, IEEE Trans. Softw. Engg. 19,1 (Jan 1993) 41–55.CrossRefGoogle Scholar
  12. [Ven90]
    Y. Venema. Expressiveness and completeness of an interval tense logic, Notre Dame J. FL 31,4 (1990) 529–547.zbMATHCrossRefMathSciNetGoogle Scholar
  13. [Ven91]
    Y. Venema. A modal logic for chopping intervals, J. Logic Comput. 1,4 (1991) 453–476.zbMATHCrossRefMathSciNetGoogle Scholar
  14. [ZHR91]
    Zhou C., C. A. R. Hoare and A. Ravn. A calculus of durations, IPL 40,5 (Dec 1991) 269–276.zbMATHCrossRefMathSciNetGoogle Scholar
  15. [ZHS93]
    Zhou C., M. R. Hansen and P. Sestoft. Decidability and undecidability results for duration calculus, Proc. STACS, LNCS 665 (1993) 58–68.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Kamal Lodaya
    • 1
  1. 1.Institute of Mathematical SciencesC.I.T. Campus, TaramaniChennaiIndia

Personalised recommendations