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Topological constraints: A representational framework for approximate spatial and temporal reasoning

  • Topology And Reasoning
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Book cover Advances in Spatial Databases (SSD 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 525))

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Abstract

This paper is based on two premises. First, real world spatial and temporal information is often imprecise and uncertain. Second, there are certain similarities between spatial and temporal reasoning which can be exploited to build an integrated reasoning framework. The latter is important because planning and reasoning usually requires consideration of both the temporal and spatial aspects of the situation under study. Topological constraints are introduced in this paper as an uniform representation schema for both spatial and temporal concepts. Fuzzy logic is used to provide the mathematical basis for representing imprecision and uncertainty.

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References

  1. Allen J. F., Maintaining Knowledge about temporal intervals, CACM, vol. 26(11), Nov. 1983

    Google Scholar 

  2. Ballard D. H., Strip trees: A Hierarchical representation for curves, CACM, vol. 24(5), pp. 310–321, 1981

    Google Scholar 

  3. Dubois D. & H. Prade, Processing Fuzzy Temporal Knowledge, IEEE Transactions on Systems, Man and Cybernetics, vol. 19, no. 4, pp. 729–744, 1989.

    Google Scholar 

  4. Dubois D., H. Prade, Possibility Theory: An approach to computerized processing of uncertainty, Plenum Press, New York, 1988

    Google Scholar 

  5. Dutta S., An Event-based Fuzzy Temporal Logic, in Proc. 18th IEEE Intl. Symp. Multiple-Valued Logic, Palma de Mallorca, Spain, 1988, pp. 64–71.

    Google Scholar 

  6. Dutta S., Approximate Reasoning with Temporal and Spatial Concepts", Ph.D. dissertation, Department of Computer Science, UC Berkeley, May 1990.

    Google Scholar 

  7. Dutta S., "Qualitative Spatial Reasoning: A Semi-Quantitative Approach Using Fuzzy Logic" in Design and Implementation of Large Spatial Databases, Lecture Notes in Computer Science, 409, A. Buchmann, O. Gunther, T.R. Smith and Y.F. Wang (Eds.), pp. 345–364, 1990.

    Google Scholar 

  8. Elfes A., Using Occupancy Grids for mobile robot perception and navigation, Computer, vol. 22(6), pp. 46–57, June 1989

    Google Scholar 

  9. Farreny H. and H. Prade, Uncertainty Handling and fuzzy logic control in navigation problems, in Proc. Intl. Conf. Intelligent Autonomous Systems, L.O. Hertzberger, F. C. A. Groen, Eds., North Holland, Amsterdam, Holland, 1987, pp. 218–225.

    Google Scholar 

  10. Freeman H., Computer Processing of line-drawing images, Computing surveys, vol. 6(1), pp. 57–97, 1974

    Google Scholar 

  11. Gadia S. K., Towards a Multihomogenous Model for a Temporal Database, In the Proc. of the International Conference on Data Engineering, 1986

    Google Scholar 

  12. Gaines B. R., Foundations of fuzzy reasoning, International Journal of Man-Machine Studies, vol. 8, pp. 623–668, 1976

    Google Scholar 

  13. Gunther O., An Expert Data-base System for the Overland Search Problem, M.S. Report, Dept. of Computer Science, UC Berkeley, 1985

    Google Scholar 

  14. Halpern J. Y., Z. Manna, B. Moszkowski, A high-level semantics based on interval logic, In Proc. ICALP, pp. 278–291, 1983

    Google Scholar 

  15. Harel D., D. Kozen, R. Parikh, Process logic: expressiveness, decidability, completeness, JCSS, vol. 25(2), pp. 145–180, Oct. 1982

    Google Scholar 

  16. Hutchins E., Understanding Micronesian Navigation, Mental models, D. Gentner and A. L. Stevens, (Eds.), pp. 191–225, Lawrence Erlbaum Associates, 1983

    Google Scholar 

  17. Kaufmann A., M. M. Gupta, Introduction to Fuzzy Arithmetic: Theory and Applications, Van Nostrand Reinhold Co., New York, NY, 1985

    Google Scholar 

  18. Kuipers B. J., T. S. Levitt, Navigation and Mapping in Large-Scale Space, AI Magazine, 1988

    Google Scholar 

  19. Kuipers B. J., Y. T. Byun, A Qualitative Approach to Robot Exploration and Map-learning, Spatial Reasoning and Multi-sensor fusion, Proc. of 1987 workshop, pp. 390–404, Morgan Kaufmann Publishers Inc., Los Altos, CA, 1987

    Google Scholar 

  20. Ladkin P., The completeness of a natural system for reasoning with time intervals, in Proc IJCAI, pp. 462–467, 1987

    Google Scholar 

  21. Levitt T., D. Lawton, D. Chelberg, P. Nelson, Qualitative Navigation, Proc. of DARPA Image Understanding Workshop, pp. 447–465, Morgan Kaufmann, Los Altos, CA, 1987

    Google Scholar 

  22. Malik J., T.O. Binford, Reasoning in time and space, in Proc IJCAI, pp. 343–345, W. Germany, 1983

    Google Scholar 

  23. Manna Z., A. Pnueli, Verification of concurrent programs: a temporal proof system, Report STAN-CS-83-967, Dept. of Computer Science, Stanford University, CA, 1983

    Google Scholar 

  24. McDermott D., A temporal logic for reasoning about processes and plans, Cognitive Science, vol. 6, pp. 101–155, 1982

    Google Scholar 

  25. McDermott D., A theory of metric spatial inference, In Proc. of AAAI, 1980

    Google Scholar 

  26. McDermott D., A. Gelsey, Terrain Analysis for Tactical Situation Assessment, Spatial Reasoning and Multi-sensor Fusion, Proc. of 1987 workshop, pp. 420–429, Morgan Kaufmann, Los Altos, CA, 1987

    Google Scholar 

  27. McDermott D., Ernest Davis, Planning and Executing Routes through Uncertain Territory, Artificial Intelligence, vol. 22, pp. 107–156, 1984

    Google Scholar 

  28. McKenzie, R. Snodgrass, Extending the Relational Algebra to support transaction time, in the Proc. of the ACM-SIGMOD International Conference on the Management of Data, 1987

    Google Scholar 

  29. McReynolds J., Geographic Orientation of the Blind, Ph.D. dissertation in U.T., 1951

    Google Scholar 

  30. Montanari U., A note on minimal length polygon approximations, CACM, vol. 13, pp. 41–47, 1970

    Google Scholar 

  31. Moszkowski B. C., Executing temporal logic programs, Cambridge University Press, 1986

    Google Scholar 

  32. Piaget J., B. Inhelder, The Child's Perception of Space, Norton, New York, 1967

    Google Scholar 

  33. Pratt V. R., Process logic, In Proc. 6th POPL, pp. 93–100, ACM, Jan. 1979

    Google Scholar 

  34. Prior A. N., Past, present and future, Clarendon Press, Oxford, 1967

    Google Scholar 

  35. Rescher N., A. Urquhart, Temporal Logic, Springer Verlag, New York, 1971

    Google Scholar 

  36. Retz-Schmidt G., Various Views on Spatial Propositions, Al Magazine, vol. 9, Summer 1988

    Google Scholar 

  37. Segev A., A. Shoshani, Logical modeling of temporal data, in the Proc. of the ACM-SIGMOD International Conference on the Management of Data, 1987

    Google Scholar 

  38. Sheng R. L., A linguistic approach to temporal information analysis, Ph.D. thesis, UC, Berkeley, 1983

    Google Scholar 

  39. Shoham Y., Reasoning about change: Time and causation from the standpoint of artificial intelligence, MIT Press, Cambridge, MA, 1988

    Google Scholar 

  40. Snodgrass R., I. Ahn, A taxonomy of time in databases, In the Proc. of the ACM SIGMOD International Conference on Management of Data, 1985

    Google Scholar 

  41. Snodgrass R., The Temporal Query Language TQuel, in the Proc. of the Third ACM SIGMOD symposium on Principles of Database systems (PODS), Waterloo, Canada, April 1984

    Google Scholar 

  42. Tsang E. P. K., Time structures for AI, Proceeding of the 10th IJCAI, 1987

    Google Scholar 

  43. Van Benthem J.F.A.K., The logic of time, D.Reidel, 1983

    Google Scholar 

  44. Vitek M., Fuzzy information and fuzzy time, Proc of IFAC, pp. 159–162, Marseille, France, 1983

    Google Scholar 

  45. Yager R.R., On different classes of linguistic variables defined via fuzzy subsets, Kybernetes, vol. 13, pp. 103–110, 1984.

    Google Scholar 

  46. Zadeh L. A., A computational approach to fuzzy quantifiers in natural languages, Computers and mathematics, vol. 9, pp. 149–184, 1983

    Google Scholar 

  47. Zadeh L. A., A theory of approximate reasoning, In Machine Intelligence, J. Hayes, D. Michie & L. I. Mikulich, Eds., vol. 9, pp. 149–194, Halstead Press, New York, 1979

    Google Scholar 

  48. Zadeh L. A., Fuzzy Sets, Information Control, vol. 8, pp. 338–353, 1965

    Google Scholar 

  49. Zadeh L. A., Test Score Semantics for Natural Languages and Meaning Representation via PRUF, Empirical Semantics (B. Reiger, Ed.), pp. 281–349, Bochum:Brockmeyer, 1982

    Google Scholar 

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Authors and Affiliations

  1. INSEAD, 77305, Fontainebleau, France

    Soumitra Dutta

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  1. Soumitra Dutta
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Oliver Günther Hans-Jörg Schek

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© 1991 Springer-Verlag Berlin Heidelberg

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Dutta, S. (1991). Topological constraints: A representational framework for approximate spatial and temporal reasoning. In: Günther, O., Schek, HJ. (eds) Advances in Spatial Databases. SSD 1991. Lecture Notes in Computer Science, vol 525. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54414-3_37

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  • DOI: https://doi.org/10.1007/3-540-54414-3_37

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54414-2

  • Online ISBN: 978-3-540-47615-3

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