Artificial Intelligence Review

, Volume 15, Issue 3, pp 189–217 | Cite as

Reified Temporal Logics: An Overview

  • J. Ma
  • B. Knight


There are three main approaches to the representationof temporal information in AI literature: theso-called method of temporal arguments thatsimply extends functions and predicates of first-orderlanguage to include time as the additional argument;modal temporal logics which are extensions ofthe propositional or predicate calculus with modaltemporal operators; and reified temporal logicswhich reify standard propositions of some initiallanguage (e.g., the classical first-order or modallogic) as objects denoting propositional terms. Theobjective of this paper is to provide an overview onthe temporal reified approach by looking closely atsome representative existing systems featuring reifiedpropositions, including those of Allen, McDermott,Shoham, Reichgelt, Galton, and Ma and Knight. We shalldemonstrate that, although reified logics might bemore complicated in expressing assertions about somegiven objects with respect to different times, theyaccord a special status to time and therefore haveseveral distinct advantages in talking about someimportant issues which would be difficult (if notimpossible) to express in other approaches.

logical formalism reification temporal logic 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Allen, J. F. (1983). Maintaining Knowledge about Temporal Intervals. Communications of the ACM 26(11): 832–843.Google Scholar
  2. Allen, J. F. (1984). Towards a General Theory of Action and Time. Artificial Intelligence 23: 123–154.Google Scholar
  3. Allen, J. F. & Ferguson, G. (1994). Actions and Events in Interval Temporal Logic. the Journal of Logic and Computation 4(5): 531–579.Google Scholar
  4. Allen, J. & Hayes, P. (1985). A Common-sense Theory of Time. Proceedings of IJCAI'95, 528–531.Google Scholar
  5. Allen, J. & Hayes, P. (1989). Moments and Points in an Interval-based Temporal-based Logic. Computational Intelligence (Canada) 5: 225–238.Google Scholar
  6. Bacchus, F., Tenenberg J. & Koomen, J. A. (1991). A Non-reified Temporal Logic. Artificial Intelligence 52: 87–108.Google Scholar
  7. Benthem, V. (1984). The Logic of Time. Dordrecht: Kluwer Academic.Google Scholar
  8. Davidson, D. (1967). The Logical form of Action Sentences. In Nicholas Rescher (ed.) The Logic of Decision and Action. University of Pittsburgh Press.Google Scholar
  9. Davidson, D. (1969). The Individuation of Events. In Nicholas Rescher (ed.) Essays in Honor of Carl G. Hempel. Dordrecht: D. Reidel.Google Scholar
  10. Gabbay, D. (1989). The Declarative Past and Executable Future. Temporal Logic in Specification: Altrincham Workshop 1987 (Lecture Notes in Computer Science) 398: 409–448.Google Scholar
  11. Galton, A. P. (1990). A Critical Examination of Allen's Theory of Action and Time. Artificial Intelligence 42: 159–188.Google Scholar
  12. Galton, A. P. (1991). Reified Temporal Theories and How to Unreify Them. Proceedings of IJCAI'91, 1177–1182.Google Scholar
  13. Galton, A. P. (1996). An Investigation of Non-intermingling Principles in Temporal Logic. Journal of Logic and Computation 6(2): 267–290.Google Scholar
  14. Gelfond, M., Lifschitz, V. & Rabinov, A. (1991). What are the Limitations of the Situation Calculus? In Working Notes of AAAI Spring Symposium Series: Logical Formalization of Commonsense Reasoning, 59–69.Google Scholar
  15. Halpern, J. Y. & Shoham, Y. (1991). A Propositional Model Logic of Time Intervals. Journal of the Association for Computing Machinery 38(4): 935–962.Google Scholar
  16. Hamblin, C. L. (1971). Instants and Intervals. Studium Generale 24: 127–134.Google Scholar
  17. Haugh, B. A. (1987). Non-Standard Semantics for the Method of Temporal Arguments. Proceedings of 10th IJCAI 1: 449–455.Google Scholar
  18. Kripke, S. (1963). Semantical Considerations on Modal Logic. Acta Philosophic, Fennica 16: 83–94.Google Scholar
  19. Lifschitz, V. (1987). A Theory of Action. Proceedings of 10th IJCAI, 966–972.Google Scholar
  20. Long, D. (1989). A Review of Temporal Logics. The Knowledge Engineering Review 4(2): 141–162.Google Scholar
  21. Ma, J. & Knight, B. (1994). A General Temporal Theory. The Computer Journal 37(2): 114–123.Google Scholar
  22. Ma, J., Knight, B. & Petridis, M. (1994). A Revised Theory of Action and Time based on Intervals and Point. The Computer Journal 37(10): 847–857.Google Scholar
  23. Ma, J. & Knight, B. (1996). A Reified Temporal Logic. The Computer Journal 39(9): 800–807.Google Scholar
  24. McArthur, R. (1976). Tense Logic. Dordrecht: Reidel.Google Scholar
  25. McCarthy, J. & Hayes, P. J. (1969). Some Philosophical Problems from the Standpoint of Artificial Intelligence. In Meltzer, B. & Michie, D. (eds.) Machine Intelligence 4: 463–502.Google Scholar
  26. McDermott, D. V. (1982). A Temporal Logic for Reasoning about Processes and Plans. Cognitive Science 6: 101–155.Google Scholar
  27. Prior, A. (1955). Diodoram Modalities. Philosophical Quarterly 5: 205–213.Google Scholar
  28. Pnueli, A. (1977). The Temporal Logic of Programs. Proceedings of 8th. IEEE Symp. On Foundations of Computer Science, 46–67.Google Scholar
  29. Reichgelt, H. (1989). A Comparison of First-order and Modal Logics of Time. In Jackson, P. and van Harmelen, H. R. F. (eds.) Logic-based Knowledge Representation, 143–176.Google Scholar
  30. Rescher, J. & Urquhart, A. (1971). Temporal Logics. Springer Verlag.Google Scholar
  31. Russell, B. (1903). Principles of Mathematics. London: George & Unwin.Google Scholar
  32. Shoham, Y. (1987). Temporal Logics in AI: Semantical and Ontological Considerations. Artificial Intelligence 33: 89–104.Google Scholar
  33. Shoham, Y. (1988). Reasoning about Change: Time and Causation from the Standpoint of Artificial Intelligence. MIT Press.Google Scholar
  34. Terenziani, P. & Torasso, P (1995). Time, Action-Types, and Causation: an Integrated Analysis. Computational Intelligence 11(3): 529–552.Google Scholar
  35. Vila, L. (1994). A Survey on Temporal Reasoning in Artificial Intelligence. AI Commun. 7: 4–28.Google Scholar
  36. Vilain,M. B. (1982). A System for Reasoning about Time. Proceedings of AAAI-82, 197–201.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • J. Ma
    • 1
  • B. Knight
    • 1
  1. 1.School of CMSUniversity of GreenwichLondonUK (E-mail

Personalised recommendations