A Temporal Logic for Successive Events

  • Conference paper
  • First Online:
Logic, Rationality, and Interaction (LORI 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14329))

Included in the following conference series:

  • 262 Accesses

Abstract

A succession of events is a sequence of events such that after one event is finished, the next one occurs successively. In this paper, we extended linear temporal logic with a new modality to capture the case that a sequence of events successively occurs. We compared the expressivity between this extended linear temporal logic and the standard linear temporal logic.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
EUR 29.95
Price includes VAT (Germany)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
EUR 53.49
Price includes VAT (Germany)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
EUR 70.61
Price includes VAT (Germany)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

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

    Article  Google Scholar 

  2. Allen, J.F., Ferguson, G.: Actions and events in interval temporal logic. In: Stock, O. (ed.) Spatial and Temporal Reasoning, pp. 205–245. Springer, Dordrecht (1997). https://doi.org/10.1007/978-0-585-28322-7_7

    Chapter  Google Scholar 

  3. Burgess, J.P.: Axioms for tense logic. II. Time periods. Notre Dame J. Formal Logic 23(4), 375–383 (1982)

    Article  Google Scholar 

  4. Gabbay, D., Pnueli, A., Shelah, S., Stavi, J.: On the temporal analysis of fairness. In: Proceedings of the 7th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 163–173 (1980)

    Google Scholar 

  5. Gerbrandy, J., Groeneveld, W.: Reasoning about information change. J. Logic Lang. Inform. 6(2), 147–169 (1997). https://doi.org/10.1023/A:1008222603071

    Article  Google Scholar 

  6. Goranko, V., Montanari, A., Sciavicco, G.: A road map of interval temporal logics and duration calculi. J. Appl. Non-Classical Logics 14(1–2), 9–54 (2004). https://doi.org/10.3166/jancl.14.9-54

    Article  Google Scholar 

  7. Goranko, V., Rumberg, A.: Temporal logic. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University, Summer 2022 edn. (2022)

    Google Scholar 

  8. Halpern, J.Y., Shoham, Y.: A propositional modal logic of time intervals. J. ACM 38(4), 935–962 (1991). https://doi.org/10.1145/115234.115351

    Article  Google Scholar 

  9. Hamblin, C.L.: Instants and intervals. In: Fraser, J.T., Haber, F.C., Müller, G.H. (eds.) The Study of Time, pp. 324–331. Springer, Heidelberg (1972). https://doi.org/10.1007/978-3-642-65387-2_23

    Chapter  Google Scholar 

  10. Hansen, M.R., Chaochen, Z.: Duration calculus: logical foundations. Formal Aspects Comput. 9, 283–330 (1997)

    Article  Google Scholar 

  11. Humberstone, I.: Interval semantics for tense logic: some remarks. J. Philos. Logic 171–196 (1979)

    Google Scholar 

  12. Kowalski, R., Sergot, M.: A logic-based calculus of events. N. Gener. Comput. 4, 67–95 (1986)

    Article  Google Scholar 

  13. Lutz, C.: Complexity and succinctness of public announcement logic. In: Proceedings of the Fifth International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS 2006, pp. 137–143. Association for Computing Machinery, New York (2006). https://doi.org/10.1145/1160633.1160657

  14. Moszkowski, B.C.: Reasoning about digital circuits. Stanford University (1983)

    Google Scholar 

  15. Plaza, J.: Logics of public communications. Synthese 158(2), 165–179 (2007)

    Article  Google Scholar 

  16. Pnueli, A.: The temporal logic of programs. In: 18th Annual Symposium on Foundations of Computer Science (SFCS 1977), pp. 46–57. IEEE (1977)

    Google Scholar 

  17. Prior, A.N.: Time and Modality. Oxford University Press, Oxford (1957)

    Google Scholar 

  18. Prior, A.N.: Present and Future. Oxford University Press, Oxford (1967)

    Book  Google Scholar 

  19. Prior, A.N.: Papers on Time and Tense. Oxford University Press, Oxford (1968)

    Google Scholar 

  20. Roper, P.: Intervals and tenses. J. Philos. Log. 9, 451–469 (1980)

    Article  Google Scholar 

  21. Van Ditmarsch, H., van Der Hoek, W., Kooi, B.: Dynamic Epistemic Logic, vol. 337. Springer, Heidelberg (2007)

    Google Scholar 

  22. Zhou, C., Hansen, M.R.: Duration Calculus: A Formal Approach to Real-Time Systems. Monographs in Theoretical Computer Science. an Eatcs Series, Springer, Heidelberg (2004)

    Google Scholar 

Download references

Acknowledgement

The authors thank four anonymous reviewers for their useful comments, which helped us to improve the presentation. This work is supported by the Fundamental Research Funds for the Central Universities (No. 63233137).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yanjun Li .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Li, Y., Zhao, J. (2023). A Temporal Logic for Successive Events. In: Alechina, N., Herzig, A., Liang, F. (eds) Logic, Rationality, and Interaction. LORI 2023. Lecture Notes in Computer Science, vol 14329. Springer, Cham. https://doi.org/10.1007/978-3-031-45558-2_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-45558-2_14

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-45557-5

  • Online ISBN: 978-3-031-45558-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Navigation