Skip to main content
SpringerLink
Log in

Continuous Temporal Models

  • Conference paper
  • First Online:
AI 2001: Advances in Artificial Intelligence (AI 2001)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2256))

Included in the following conference series:

Abstract

We develop notation for describing a temporal structure over the real numbers flow of time. This forms a basis for various reasoning tasks including synthesizing a model from a given temporal or first-order specification. We announce an efficient procedure for finding a manageable description of such a model. There are applications in reasoning about multi-agent systems, understanding natural language, analogue devices, robotics and artificial reasoning.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Allen, H. Kautz, R. Pelavin, and J. Tenenberg. Reasoning about Plans. Morgan Kaufman, 1991.

    Google Scholar 

  2. J. F. Allen. Towards a general theory of action and time. Artificial Intelligence, 23(2):123–154, 1984.

    Article  MATH  Google Scholar 

  3. R. Alur and T. A. Henzinger. Real-time logics: Complexity and expressiveness. Information and Control, 104:35–77, 1993.

    MATH  MathSciNet  Google Scholar 

  4. H. Barringer, M. Fisher, D. Gabbay, R. Owens, and M. Reynolds, editors. The Imperative Future. Research Studies Press, Somerset, 1996.

    Google Scholar 

  5. H. Barringer, R. Kuiper, and A. Pnueli. A really abstract concurrent model and its temporal logic. In Proceedings of 13th ACM symposium on the principles of Programming Languages, St. Petersberg Beach, Florida, January 1986.

    Google Scholar 

  6. H. Bowman, H. Cameron, and S. Thompson. Specification and prototyping of structured multimedia documents using interval temporal logic. In H. Barringer, M. Fisher, D. Gabbay, and G. Gough, editors, Advances in Temporal Logic, pages 435–453. Kluwer, 2000.

    Google Scholar 

  7. H. Bowman and S. Thompson. A tableaux method for interval temporal logic with projection. In TABLEAUX’98, volume 1397 of LNAI, pages 108–123. Springer Verlag, 1998.

    Google Scholar 

  8. J. P. Burgess and Y. Gurevich. The decision problem for linear temporal logic. Notre Dame J. Formal Logic, 26(2):115–128, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  9. J. Fiadeiro and T. Maibaum. Sometimes “tomorrow” is “sometime” — action refinement in a temporal logic of objects. In D. Gabbay and H. Ohlbach, editors, Temporal Logic, Proceedings of ICTL’94, number 827 in LNAI, pages 48–66. Springer-Verlag, 1994.

    Google Scholar 

  10. D. Gabbay, I. Hodkinson, and M. Reynolds. Temporal Logic: Mathematical Foundations and Computational Aspects, Volume 1. Oxford University Press, 1994.

    Google Scholar 

  11. D. M. Gabbay and I. M. Hodkinson. An axiomatisation of the temporal logic with until and since over the real numbers. J. Logic and Computation, 1(2):229–260, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  12. D. M. Gabbay, I. M. Hodkinson, and M. A. Reynolds. Temporal expressive completeness in the presence of gaps. In J. Oikkonen and J. Väänänen, editors, Logic Colloquium’ 90, Proceedings ASLEur opean Meeting 1990, Helsinki, number 2 in Lecture Notes in Logic, pages 89–121. Springer-Verlag, 1993.

    Google Scholar 

  13. D. Gabbay, M. Reynolds, and M. Finger. Temporal Logic: Mathematical Foundations and Computational Aspects, Vol. 2. Oxford University Press, 2000.

    Google Scholar 

  14. J. Halpern and Y. Shoham. A propositional modal logic of time intervals. In Proceedings, Symposium on Logic in Computer Science. IEEE, Boston, 1986.

    Google Scholar 

  15. H. Kamp. Tense logic and the theory of linear order. PhD thesis, University of California, Los Angeles, 1968.

    Google Scholar 

  16. Y. Kesten, Z. Manna, and A. Pnueli. Temporal verification of simulation and refinement. In J. de Bakker, W. de Roover, and G. Rozenberg, editors, A decade of concurrency, pages 273–346. Springer-Verlag, 1994.

    Google Scholar 

  17. M. Marx, S. Mikulas, and M. Reynolds. The mosaic method for temporal logics. In R. Dyckho., editor, Proceedings of TABLEAUX 2000, Saint Andrews, Scotland, July 2000, pages 324–340. Springer, 2000.

    Google Scholar 

  18. M. Leith and J. Cunningham. Modelling linguistic events. In H. Barringer, M. Fisher, D. Gabbay, and G. Gough, editors, Advances in Temporal Logic, pages 207–222. Kluwer, 2000.

    Google Scholar 

  19. M. Moens and M. Steedman. Temporal ontology and temporal reference. Journal of Computational Linguistics, 14, 1988.

    Google Scholar 

  20. A. Montanari, A. Peron, and A. Policriti. Extending Kamp theorem to linear orders with binary predicates to model time granularity. In ICTL2000, Proceedings of the Third International Conference on Temporal Logic, 2000.

    Google Scholar 

  21. B. Moszkowski. Executing Temporal Logic Programs. Cambridge, 1986.

    Google Scholar 

  22. B. Nebel and C. Bäckström. On the computational complexity of temporal projection, planning, and plan validation. Artificial Intelligence, 66(1):125–160, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  23. B. Nebel and H-J. Bürckert. Reasoning about temporal relations: A maximal tractable subclass of Allen’s interval algebra. J. of the ACM, 42(1):43–66, January 1995.

    Article  MATH  Google Scholar 

  24. J. Ostroff. Composition and refinement of discrete real-time systems. Technical report, DCS, York University, Ontario, Canada, 1998. CS-1998-10.

    Google Scholar 

  25. A. Pnueli. The temporal logic of programs. In 18th Symposium on Foundations of Computer Science, pages 46–57, 1977. Providence, RI.

    Google Scholar 

  26. A. Pnueli and R. Rosner. On the synthesis of an asynchronous reactive module. In ICALP89, volume 372 of LNCS, pages 652–671. Springer-Verlag, 1989.

    Google Scholar 

  27. V. R. Pratt. Models of program logics. In Proc. 20th IEEE. Symposium on Foundations of Computer Science, San Juan, pages 115–122, 1979.

    Google Scholar 

  28. A. Rabinovich. On the decidability of continuous time specification formalisms. Journal of Logic and Computation, 8:669–678, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  29. M. Reynolds. An axiomatization for Until and Since over the reals without the IRR rule. Studia Logica, 51:165–193, May 1992.

    Google Scholar 

  30. M. Reynolds. A decidable temporal logic of parallelism. Notre Dame Journal of Formal Logic, 38(3):419–436, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  31. M. Reynolds. Synthesis of a continuous temporal model, in preparation.

    Google Scholar 

  32. M. Reynolds. The complexity of the temporal logic over the reals, submitted. Version available at http://www.it.murdoch.edu.au/~mark/research/online.

  33. P. Rodrigues, J. Felix Costa and H. Sigelmann. Verifying Properties of Neural Networks. In J. Mira Mira, editor, IWANN2001, 6th International Work-Conference on Artificial and Natural Neural Networks, LNCS, Springer-Verlag, 2001.

    Google Scholar 

  34. A. Sistla and E. Clarke. Complexity of propositional linear temporal logics. J. ACM, 32:733–749, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  35. A. Sistla and L. Zuck. Reasoning in a Restricted Temporal Logic. Information and Computation, 102:167–195, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  36. O. Stock, editor. Spatial and Temporal Resaoning. Kluwer, 1997.

    Google Scholar 

  37. L. Stockmeyer. The complexity of decision problems in automata and logic. PhD thesis, M.I.T., 1974.

    Google Scholar 

  38. J. van Benthem. Temporal logic. In D.M. Gabbay, C.J. Hogger, and J.A. Robinson, editors, The Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 4, Oxford University Press, 1995.

    Google Scholar 

  39. Y. Venema. Completeness through flatness in two-dimensional temporal logic. In D. Gabbay and H.-J. Ohlbach, editors, Temporal Logic, First International Conference, ICTL’94, volume 827 of LNAI, pages 149–164. Springer-Verlag, 1994.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Murdoch University, 6150, Murdoch, Perth, W.A., Australia

    Mark Reynolds

Authors
  1. Mark Reynolds
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Computer and Information Science, University of South Australia, Mawson Lakes, 5095, SA, Australia

    Markus Stumptner  & Dan Corbett  & 

  2. Department of Computer Science, University of Adelaide, 5001, Adelaide, SA, Australia

    Mike Brooks

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Reynolds, M. (2001). Continuous Temporal Models. In: Stumptner, M., Corbett, D., Brooks, M. (eds) AI 2001: Advances in Artificial Intelligence. AI 2001. Lecture Notes in Computer Science(), vol 2256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45656-2_36

Download citation

  • DOI: https://doi.org/10.1007/3-540-45656-2_36

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42960-9

  • Online ISBN: 978-3-540-45656-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation