Formulating the Temporal Causal Relationships Between Events and Their Results

  • J. MaEmail author
  • M. Petridis
  • B. Knight
Conference paper


We introduce in this paper a formalism for representing flexible temporal causal relationships between events and their effects. A formal characterization of the so-called (most) General Temporal Constraint (GTC) is formulated, which guarantees the common-sense assertion that “the beginning of the effect cannot precede the beginning of its causal event”. It is shown that there are actually in total 8 possible temporal causal relationships which satisfy the GTC. These include cases where, (1) the effect becomes true immediately after the end of the event and remains true for some time after the event; (2) the effect holds only over the same time over which the event is in progress; (3) the beginning of the effect coincides with the beginning of the event, and the effect ends before the event completes; (4) the beginning of the effect coincides with the beginning of the event, and the effect remains true for some time after the event; (5) the effect only holds over some time during the progress of the event; (6) the effect becomes true during the progress of the event and remains true until the event completes; (7) the effect becomes true during the progress of the event and remains true for some time after the event; and (8) where there is a time delay between the event and its effect. We shall demonstrate that the introduced formulation is versatile enough to subsume those existing representative formalisms in the literature.


Order Relation Temporal Relation Meeting Place Time Element Negative Sentence 
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.


  1. 1.
    McCarthy, J., Situations, actions and causal laws, Stanford Artificial Intelligence Project: Memo 2, 1963.Google Scholar
  2. 2.
    McCarthy, J., Hayes, P.: Some philosophical problems from the standpoint of artificial intelligence, in Machine Intelligence, 4, Eds. Meltzer B. and Michie D., Edinburgh University Press, pages 463–502, 1969.Google Scholar
  3. 3.
    McDermott, D.: A Temporal Logic for Reasoning about Processes and Plans, Cognitive Science, 6: 101–155, 1982.Google Scholar
  4. 4.
    Allen, J.: Maintaining Knowledge about Temporal Intervals, Communication of ACM, 26: 832–843, 1983.Google Scholar
  5. 5.
    Allen, J.: Towards a General Theory of Action and Time, Artificial Intelligence, 23: 123–154, 1984.Google Scholar
  6. 6.
    Kowalski, R., Sergot, M.: A Logic-based Calculus of Events, New Generation Computing, 4: 67–95, 1986.Google Scholar
  7. 7.
    Shoham, Y.: Temporal logics in AI: Semantical and Ontological Considerations, Artificial Intelligence, 33: 89–104, 1987.Google Scholar
  8. 8.
    Shoham, Y.: Reasoning about Change: Time and Causation from the Standpoint of Artificial Intelligence, MIT Press, 1988.Google Scholar
  9. 9.
    Terenziani, P., Torasso, P.: Time, Action-Types, and Causation: an Integrated Analysis, Computational Intelligence, 11(3): 529–552, 1995.Google Scholar
  10. 10.
    Lifschitz, V.: Formal theories of action, In Proceedings of the Tenth International Joint Conference on, Artificial Intelligence, pages 966–972, 1987.Google Scholar
  11. 11.
    Sandewall, E.: Filter preferential entailment for the logic of action in almost continuous worlds. In Proceedings of the 12th International Joint Conference on, Artificial Intelligence, pages 894–899, 1989].Google Scholar
  12. 12.
    Schubert, L.: Monotonic Solution of the Frame Problem in the Situation Calculus: an Efficient Method for Worlds with Fully Specified Actions, in: H.E. Kyburg, R. Loui and G. Carlson, eds., Knowledge Representation and Defeasible Reasoning, pages 23–67, Kluwer Academic Press, 1990.Google Scholar
  13. 13.
    Gelfond, M., Lifschitz, V., Rabinov, A.: What are the Limitations of the Situation Calculus? In Working Notes of AAAI Spring Symposium Series. Symposium: Logical Formalization of Commonsense Reasoning, pages 59–69, 1991.Google Scholar
  14. 14.
    Lin, F., Shoham, Y.: Concurrent Actions in the Situation Calculus, In Proceedings of AAAI-92, pages 590–595, 1992.Google Scholar
  15. 15.
    Pinto, J., Reiter, R.: Temporal Reasoning in Logic Programming: A Case for the Situation Calculus, In Proceedings of 10th Int. Conf. on Logic Programming, Budapest, Hungary, pages 21–24, 1993.Google Scholar
  16. 16.
    Pinto, J., Reiter, R.: Reasoning about Time in the Situation Calculus, Annals of Mathematics and Artificial Intelligence, 14(2–4): 251–268, 1995.Google Scholar
  17. 17.
    Miller, R., Shanahan, M.: Narratives in the Situation Calculus, the Journal of Logic and Computation, 4(5): 513–530, 1994.Google Scholar
  18. 18.
    Shanahan, M.: A Circumscriptive Calculus of Events, Artificial Intelligence, 77: 29–384, 1995.Google Scholar
  19. 19.
    Baral, C.: Reasoning about actions: non-deterministic effects, constraints, and qualification, In Proceedings of IJCAI’95, pages 2017–2023, 1995.Google Scholar
  20. 20.
    Baral, C., Gelfond, M.: Reasoning about Effects of Concurrent Actions, Journal of Logic Programming, 31(1–3): 85–117, 1997.Google Scholar
  21. 21.
    Baral, C., Son, T., Tuan, L.: A transition function based characterization of actions with delayed and continuous effects, In Proceedings of KR’02, pages 291–302, 2002.Google Scholar
  22. 22.
    Allen J., Ferguson, G.: Actions and Events in Interval Temporal Logic, the Journal of Logic and Computation, 4(5): 531–579, 1994.Google Scholar
  23. 23.
    Ma, J., Knight, B.: A Reified Temporal Logic, the Computer Journal, 39(9): 800–807, 1996.Google Scholar
  24. 24.
    Ma, J., Knight, B.: A General Temporal Theory, the Computer Journal, 37(2): 114–123, 1994.Google Scholar
  25. 25.
    van Benthem, J.: The Logic of Time, Kluwer Academic, Dordrech, 1983.Google Scholar
  26. 26.
    Galton, A.: A Critical Examination of Allen’s Theory of Action and Time, Artificial Intelligence, 42: 159–188, 1990.Google Scholar
  27. 27.
    Vila, L.: A survey on temporal Reasoning in Artificial Intelligence. AI Communications, 7: 4–28, 1994.Google Scholar
  28. 28.
    Ma, J., Hayes, P.: Primitive Intervals Vs Point-Based Intervals: Rivals Or Allies? the Computer Journal, 49: 32–41, 2006.Google Scholar
  29. 29.
    Allen J., Hayes, P.: Moments and Points in an Interval-based Temporal-based Logic, Computational Intelligence, 5: 225–238, 1989.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.University of GreenwichLondonUk
  2. 2.University of BrightonBrightonUk

Personalised recommendations