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Ordering events: Intervals are sufficient, more general sets are usually not necessary

Для упорядочивания событий достаточно интервалов, более общие виды множеств, как правило, не нужны

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Reliable Computing

Abstract

Traditionally, an interval is used to describe incomplete knowledge about a moment of time when an event occured. In principle, more general sets are sometimes needed to describe our knowledge. In this paper, we show that if we are only interested in the ordering of events, then intervals are sufficient. This result provides one more justification for the use of the intervals.

Abstract

Как нравило, для представленяя нецолното энания о моменте времени, в который проиэошло некоторое событие, иснольэуется интервал. В припцице, иногда для представления энаний требуются более общие биды множеств. В работе покаэано, что для решения эадачи упорядочивания событий достаточно интервалов. Таким обраэом, дается еще одно обоснование испольэования интервалов.

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References

  1. Allen, J.Maintaining knowledge about temporal intervals. Communications of the ACM26 (1983), pp. 832–843 (reprinted in [12]).

    Article  MATH  Google Scholar 

  2. Allen, J.Towards a general theory of action and time. Artificial Intelligence23 (1984), pp. 123–154.

    Article  MATH  Google Scholar 

  3. Allen, J. and Hayes, P.A common-sense theory of time. In: “Proceedings of the 9th International Joint Conference on Artificial Intelligence”, Los Angeles, 1985, pp. 528–531.

  4. Allen, J. F. and Kautz, H. A.A model of naive temporal reasoning. In: Hobbs, J. R. and Moore, R. C. (eds) “Formal Theories of the Commonsense World”, Ablex, Norwood, NJ, 1985, pp. 251–268.

    Google Scholar 

  5. Cervesato, I., Montanari, A., and Provetti, A.On the non-monotonic behaviour of event calculus for deriving maximal time intervals. Interval Computations2 (1993), pp. 83–119.

    MathSciNet  Google Scholar 

  6. Gelfond, M. and Przymusinska, H.Towards a theory of elaboration tolerance: logic programming approach. Int. Journal of Software Engineering and Knowledge Engineering: a Special Issue on Knowledge Representation Methods (1995) (to appear).

  7. Hammer, R., Hocks, M., Kulisch, U., and Ratz, D.Numerical toolbox for verified computing. I. Basic numerical problems. Springer Verlag, Heidelberg, N.Y., 1993.

    Google Scholar 

  8. Kearfott, R. B. and Kreinovich, V. (eds)Applications of interval computations. Kluwer, Dordrecht, Boston, 1996.

    Google Scholar 

  9. Kreinovich, V. (ed.)Extended abstracts of APIC'95: international workshop on applications of interval computations, El Paso, TX, Febr. 23–25, 1995. Reliable Computing (1995), Supplement.

  10. Kreinovich, V.Why intervals? A simple limit theorem that is similar to limit theorems from statistics. Reliable Computing1 (1) (1995), pp. 33–40.

    Article  MATH  MathSciNet  Google Scholar 

  11. McCarthy, J.Program with common sense. In: “Proceedings of the Teddington Conference on the Mechanization of Thought Processes”, London, Her Majesty's Stationary Office, 1959, pp. 75–91; reprinted in Lifschitz, V. (ed.) “Formalizing Common Sense. Papers by John McCarthy”, Ablex, Norwood, NJ, 1990, pp. 9–20.

    Google Scholar 

  12. Weld, D. and de Kleer, J.Qualitative reasoning about physical systems. Morgan Kaufmann, San Mateo, CA, 1989.

    Google Scholar 

  13. Wiener, N.A contribution to the theory of relative position. In: “Proc. Cambridge Philos. Soc.”17 (1914), pp. 441–449.

    MATH  Google Scholar 

  14. Wiener, N.A new theory of measurement: a study in the logic of mathematics. In: “Proceedings of the the London Mathematical Society”19 (1921), pp. 181–205.

    Google Scholar 

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© A. Provetti, 1996

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Provetti, A. Ordering events: Intervals are sufficient, more general sets are usually not necessary. Reliable Comput 2, 321–327 (1996). https://doi.org/10.1007/BF02391703

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  • DOI: https://doi.org/10.1007/BF02391703

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