Maximal intervals: An approach to temporal reasoning

  • Cristina Ribeiro
  • António Porto
Temporal Reasoning
Part of the Lecture Notes in Computer Science book series (LNCS, volume 541)


Temporal reasoning is recognized as a key problem in many AI areas, namely knowledge bases, natural language processing and planning. The ability to deal with partial knowledge is particularly important in a temporal domain. We describe a temporal language that accounts for incompletely specified temporal information about propositions. The language is semantically based on the notion of maximal interval, the denotation of a proposition being a set of maximal intervals where it holds. The main differences between classical formalisms such as those by Allen, McDermott, Shoham and Kowalski and our approach are briefly discussed. In a partial KB, abduction on the temporal order is generally needed to answer a query, and the answer is then conditional on the abduced facts. To comply with the intended semantics, an implicit form of temporal consistency has to be enforced, and this presents the main challenge to the design of the inference mechanism. We present here the syntax and declarative semantics of a propositional version of the language of maximal intervals and a first discussion of the problems in designing an inference system adequate to work with this temporal framework.


temporal reasoning knowledge representation deductive databases 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [All83]
    James Allen. Maintaining Knowledge About Temporal Intervals. Communications of the ACM, 26(11):832–843, 1983.Google Scholar
  2. [All84]
    James Allen. Towards a General Theory of Action and Time. Artificial Intelligence, (23):123–154, 1984.Google Scholar
  3. [HM86]
    Steve Hanks and Drew McDermott. Default reasoning, nonmonotonic logics and the frame problem. In Proceedings of the 5th National Conference on Artificial Intelligence, pages 328–333, AAAI, 1986.Google Scholar
  4. [KS86]
    Robert Kowalski and Marek Sergot. A logic-based calculus of events. New Generation Computing, 4(1):67–95, 1986.Google Scholar
  5. [Lad86]
    Peter Ladkin. Time representation: a taxonomy of interval relations. In Proceedings of the 5th National Conference on Artificial Intelligence, pages 360–366, 1986.Google Scholar
  6. [McD82]
    Drew McDermott. A Temporal Logic for Reasoning About Processes and Plans. Cognitive Science, (6):101–155, 1982.Google Scholar
  7. [MH81]
    J. M. McCarthy and P. J. Hayes. Some Philosophical Problems from the Standpoint of Artificial Intelligence. Readings in Artificial Intelligence, 1981.Google Scholar
  8. [PR90a]
    António Porto and Cristina Ribeiro. Maximal Intervals: A Logic of Temporal Information. Technical Report DI-28, Departamento de Informática, FCT-UNL, 1990.Google Scholar
  9. [PR90b]
    António Porto and Cristina Ribeiro. Representação de conhecimentos acerca de eventos temporais. In Actas do 2 o Congresso Iberoamericano de Inteligência Artificial, 1990.Google Scholar
  10. [Sho87]
    Yoav Shoham. Reasoning about Change. The MIT Press, 1987.Google Scholar
  11. [vB83]
    J. F. A. K. van Benthem. The logic of time. Volume 156 of Studies in Epistemology, Logic, Methodology and Philosophy of Science, D. Reidel Publishing Company, 1983.Google Scholar
  12. [vB89]
    Peter van Beek. Approximation algorithms for temporal reasoning. In Proceedings of the 11th International Joint Conference on Artificial Intelligence, pages 1291–1296, 1989.Google Scholar
  13. [VK86]
    Marc Vilain and Henry Kautz. Constraint propagation algorithms for temporal reasoning. In Proceedings of the 5th National Conference on Artificial Intelligence, pages 377–382, 1986.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Cristina Ribeiro
    • 1
  • António Porto
    • 1
  1. 1.Departamento de InformáticaUniversidade Nova de LisboaMonte da CaparicaPortugal

Personalised recommendations