Skip to main content
SpringerLink
Log in

Sharpening the Undecidability of Interval Temporal Logic

  • Conference paper
  • First Online:
Book cover Advances in Computing Science — ASIAN 2000 (ASIAN 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1961))

Included in the following conference series:

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. F. Allen. Maintaining knowledge about temporal intervals, Commun. ACM 26,11 (Nov 1983) 832–843.

    Article  MATH  Google Scholar 

  2. 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. J. P. Burgess. Axioms for tense logic II: time periods, Notre Dame J. FL 23,4 (Oct 1982) 375–383.

    Article  MATH  MathSciNet  Google Scholar 

  4. B. Dutertre. On first order interval temporal logic, Tech Report, Royal Holloway College, University of London (1995), http://www.csl.sri.com/~bruno/publis/ TR-CSD-94-3.ps.gz. [Also in Proc. 10th LICS (1995).]

  5. 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. J. Y. Halpern and Y. Shoham. A propositional modal logic of time intervals, J. ACM 38,4 (Oct 1991) 935–962.

    Article  MATH  MathSciNet  Google Scholar 

  7. 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. P. K. Pandya. Some extensions to propositional meanvalue calculus: expressiveness and decidability, Proc. CSL, LNCS 1092 (1995) 434–451.

    Google Scholar 

  9. A. Rabinovich. On the decidability of continuous time specification formalisms, J. Logic Comput. 8,5 (1998) 669–678.

    Article  MATH  MathSciNet  Google Scholar 

  10. R. Rosner and A. Pnueli. A choppy logic, Proc. 1st LICS (1986) 306–313.

    Google Scholar 

  11. 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.

    Article  Google Scholar 

  12. Y. Venema. Expressiveness and completeness of an interval tense logic, Notre Dame J. FL 31,4 (1990) 529–547.

    Article  MATH  MathSciNet  Google Scholar 

  13. Y. Venema. A modal logic for chopping intervals, J. Logic Comput. 1,4 (1991) 453–476.

    Article  MATH  MathSciNet  Google Scholar 

  14. Zhou C., C. A. R. Hoare and A. Ravn. A calculus of durations, IPL 40,5 (Dec 1991) 269–276.

    Article  MATH  MathSciNet  Google Scholar 

  15. Zhou C., M. R. Hansen and P. Sestoft. Decidability and undecidability results for duration calculus, Proc. STACS, LNCS 665 (1993) 58–68.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematical Sciences, C.I.T. Campus, Taramani, 600 113, Chennai, India

    Kamal Lodaya

Authors
  1. Kamal Lodaya
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. International Institute for Software Technology, United Nations University, Casa Silva Mendes,Estrada do Engenheiro Trigo NO 4, Macau, China

    He Jifeng

  2. Graduate School of Informatics, Kyoto University, 606-8501, Kyoto, Sakyo-ku, Japan

    Masahiko Sato

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lodaya, K. (2000). Sharpening the Undecidability of Interval Temporal Logic. In: Jifeng, H., Sato, M. (eds) Advances in Computing Science — ASIAN 2000. ASIAN 2000. Lecture Notes in Computer Science, vol 1961. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44464-5_21

Download citation

  • DOI: https://doi.org/10.1007/3-540-44464-5_21

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41428-5

  • Online ISBN: 978-3-540-44464-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation