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Approximate Qualitative Temporal Reasoning

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Abstract

We partition the time-line in different ways, for example, into minutes, hours, days, etc. When reasoning about relations between events and processes we often reason about their location within such partitions. For example, x happened yesterday and y happened today, consequently x and y are disjoint. Reasoning about these temporal granularities so far has focussed on temporal units (relations between minute, hour slots). I shall argue in this paper that in our representations and reasoning procedures we need into account that events and processes often lie skew to the cells of our partitions. For example, ‘happened yesterday’ does not mean that x started at 12 a.m. and ended 0 p.m. This has the consequence that our descriptions of temporal location of events and processes are often approximate and rough in nature rather than exact and crisp. In this paper I describe representation and reasoning methods that take the approximate character of our descriptions and the resulting limits (granularity) of our knowledge explicitly into account.

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References

  1. J.F. Allen, Maintaining knowledge about temporal intervals, Communications of the ACM 26(11) (1983) 832-843.

    Google Scholar 

  2. T. Bittner, Rough sets in spatio-temporal data mining, in: International Workshop on Temporal, Spatial, and Spatio-Temporal Data Mining, eds. K. Hornsby and J. Roddick, Lecture Notes in Artificial Intelligence, Vol. 2007 (Springer, 2001).

  3. C. Bettini, S. Jajodia and X.S. Wang, Time Granularities in Databases, Data Mining, and Temporal Reasoning (Springer, 2000).

  4. T. Bittner and B. Smith, A taxonomy of granular partitions, in: Proceedings of the Conference on Spatial Information Theory (COSIT 2001), Lecture Notes in Computer Science (Springer, 2001).

  5. T. Bittner and B. Smith, Vagueness and granular partitions, in: Proceedings of the 2nd International Conference on Formal Ontology in Information Systems (FOIS 2001) (Sheridan Printing Company, 2001).

  6. T. Bittner and J.G. Stell, A boundary-sensitive approach to qualitative location, Annals of Mathematics and Artificial Intelligence 24 (1998) 93-114.

    Google Scholar 

  7. T. Bittner and J.G. Stell, Rough sets in approximate spatial reasoning, in: Proceedings of the 2nd International Conference on Rough Sets and Current Trends in Computing (RSCTC'2000), Lecture Notes in Computer Science (Springer, 2000).

  8. T. Bittner and J.G. Stell, Rough location of vague objects, Geoinformatica (2001).

  9. C. Bettini, X. Wang and S. Jajodia, A general framework for time granularity and its application to temporal reasoning, Annals of Mathematics and Artificial Intelligence 22 (1998) 29-58.

    Google Scholar 

  10. R. Casati and A. Varzi, The structure of spatial localization, Philosophical Studies 82(2) (1995) 205-239.

    Google Scholar 

  11. L. Chittaro and C. Combi, Extending the event calculus with temporal granularity and indeterminacy, in: Proceedings of the AAAI 2000 Workshop on Spatial and Temporal Granularity, Austin, TX (AAAI Press, Menlo Park, CA, 2000).

    Google Scholar 

  12. L. Chittaro and A. Montanari, Temporal representation and reasoning in artificial intelligence: issues and approaches, Annals of Mathematics and Artificial Intelligence 28 (2000).

  13. E. Ciapessoni, E. Corsetti, A. Montanari and P. San Pietro, Embedding time granularity in a logical specification language for synchronous real-time systems (1993).

  14. A.G. Cohn, B. Bennett, J. Goodday and N. Gotts, Qualitative spatial representation and reasoning with the region connection calculus, Geoinformatica 1(3) (1997) 1-44.

    Google Scholar 

  15. A.G. Cohn, J.M. Gooday and B. Bennett, A comparison of structures in spatial and temporal logics, in: Philosophy and the Cognitive Science: Proceedings of the 16th International Wittgenstein Symposium, eds. R. Casti, B. Smith and G. White (Hölder-Pichler-Tempsky, 1994).

  16. A.G. Cohn and N.M. Gotts, The 'egg-yolk' representation of regions with indeterminate boundaries, in: Geographic Objects with Indeterminate Boundaries, GISDATA Series II, eds. P. Burrough and A.U. Frank (Taylor & Francis, London, 1996).

    Google Scholar 

  17. C. Combi, F. Pinciroli and G. Pozzi, Managing different time granularities of clinical information by an interval-based temporal data model, Methods of Information in Medicine 34(5) (1995) 458-474.

    Google Scholar 

  18. C. Combi, Representing absolute time expressions with vagueness, indeterminacy, and different granularities, in: Proceedings of the AAAI 2000 Workshop on Spatial and Temporal Granularity, Austin, TX, USA (AAAI Press, Menlo Park, CA, 2000).

    Google Scholar 

  19. E. Corsetti, A. Montanari and E. Ratto, Dealing with different granularities in formal specifications of real-time systems, Journal of Real-Time Systems 3(2) (1991).

  20. C. Dyreson and R. Snodgrass, Temporal granularity, in: The TSQL2 Temporal Query Language, ed. R.T. Snodgrass (Kluwer Academic, 1995) pp. 347-385.

  21. M.J. Egenhofer and R.D. Franzosa, Point-set topological spatial relations, International Journal of Geographical Information Systems 5(2) (1991) 161-174.

    Google Scholar 

  22. J. Euzenat, An algebraic approach for granularity in qualitative space and time representation, in: Proceedings of the IJCAI-95 (1995) pp. 894-900.

  23. A.U. Frank, Qualitative temporal reasoning in GIS-ordered time scales, in: SDH, Edinburgh, Scotland, UK, Vol. 1, eds. T.C. Waugh and R.G. Healey (Taylor & Francis, 1994).

  24. C. Freksa, Temporal reasoning based on semi-intervals, Artificial Intelligence 54 (1992) 199-227.

    Google Scholar 

  25. P. Geach, Some problems about time, Proceedings of the British Academy 11 (1966).

  26. J.M. Goodday and A.G. Cohn, Conceptual neighborhoods in temporal and spatial reasoning, in: ECAI-94 Spatial and Temporal Reasoning Workshop (1994).

  27. I.A. Goralwalla, Y. Leontiev, M.T. Özsu, D. Szafron and C. Combi, Temporal granularity for unanchored temporal data, in: Proceedings of the 1998 ACM CIKM International Conference on Information and Knowledge Management, Bethesda, Maryland, USA, November 3-7, eds. G. Gardarin, J.C. French, N. Pissinou, K. Makki and L. Bouganim (ACM, 1998) pp. 414-423.

  28. J. Hobbs, Granularity, in: Proceedings of the IJCAI 85 (1985) pp. 432-435.

  29. P. Ladkin, Time representation: A taxonomy of interval relations, in: Proceedings of AAAI-86, Philadelphia (1986) pp. 360-366.

  30. P. Ladkin, The logic of time representation, Ph.D. thesis, University of California (1987).

  31. R. Laurini and D. Thompson, Fundamentals of Spatial Information Systems, The APIC Series (Academic Press, 1994).

  32. G. Ligozat, Generalized intervals: a guided tour, in: Proceedings of the ECAI-98 Workshop on Spatial and Temporal Reasoning, Brighton, UK (1998).

  33. J. McTaggart, The Nature of Existence, Vol. II (Cambridge University Press, 1927).

  34. Z. Pawlak, Rough sets, International Journal of Computational Informatics 11 (1982) 341-356.

    Google Scholar 

  35. Z. Pawlak, Rough Sets: Theoretical Aspects of Reasoning about Data, Theory and Decision Library, Series D, System Theory, Knowledge Engineering, and Problem Solving, Vol. 9 (Kluwer Academic, Dordrecht/Boston, 1991).

    Google Scholar 

  36. D.A. Randell, Z. Cui and A.G. Cohn, A spatial logic based on regions and connection, in: 3rd International Conference on Knowledge Representation and Reasoning (Boston, 1992).

  37. J. Renz and B. Nebel, On the complexity of qualitative spatial reasoning: amaximal tractable fragment of the region connection calculus, Artificial Intelligence 108(1-2) (1999) 69-123.

    Google Scholar 

  38. P. Simons, Parts, a Study in Ontology (Clarendon Press, Oxford, 1987).

    Google Scholar 

  39. B. Smith, On drawing lines on a map, in: Conference on Spatial Information Theory, eds. A.U. Frank and W. Kuhn, Semmering, Austria, COSIT, Vol. 988 (Springer, 1995).

  40. B. Smith, Fiat objects, Topoi 20(2) (2001).

  41. B. Smith and B. Brogaard, Quantum mereotopology, Annals of Mathematics and Artificial Intelligence 36(1-2) (2002) 153-175.

    Google Scholar 

  42. A.C. Varzi, On the boundary between mereology and topology, in: Philosophy and the Cognitive Science, eds. R. Casati, B. Smith and G. White (Hölder-Pichler-Tempsky, 1994) pp. 423-442.

  43. M.F. Worboys, Imprecision in finite resolution spatial data, Geoinformatica (1998).

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Authors and Affiliations

  1. Qualitative Reasoning Group, Department of Computer Science, Northwestern University, USA

    Thomas Bittner

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  1. Thomas Bittner
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Bittner, T. Approximate Qualitative Temporal Reasoning. Annals of Mathematics and Artificial Intelligence 36, 39–80 (2002). https://doi.org/10.1023/A:1015899702951

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