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
Allen J. F., Maintaining Knowledge about temporal intervals, CACM, vol. 26(11), Nov. 1983
Ballard D. H., Strip trees: A Hierarchical representation for curves, CACM, vol. 24(5), pp. 310–321, 1981
Dubois D. & H. Prade, Processing Fuzzy Temporal Knowledge, IEEE Transactions on Systems, Man and Cybernetics, vol. 19, no. 4, pp. 729–744, 1989.
Dubois D., H. Prade, Possibility Theory: An approach to computerized processing of uncertainty, Plenum Press, New York, 1988
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.
Dutta S., Approximate Reasoning with Temporal and Spatial Concepts", Ph.D. dissertation, Department of Computer Science, UC Berkeley, May 1990.
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.
Elfes A., Using Occupancy Grids for mobile robot perception and navigation, Computer, vol. 22(6), pp. 46–57, June 1989
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.
Freeman H., Computer Processing of line-drawing images, Computing surveys, vol. 6(1), pp. 57–97, 1974
Gadia S. K., Towards a Multihomogenous Model for a Temporal Database, In the Proc. of the International Conference on Data Engineering, 1986
Gaines B. R., Foundations of fuzzy reasoning, International Journal of Man-Machine Studies, vol. 8, pp. 623–668, 1976
Gunther O., An Expert Data-base System for the Overland Search Problem, M.S. Report, Dept. of Computer Science, UC Berkeley, 1985
Halpern J. Y., Z. Manna, B. Moszkowski, A high-level semantics based on interval logic, In Proc. ICALP, pp. 278–291, 1983
Harel D., D. Kozen, R. Parikh, Process logic: expressiveness, decidability, completeness, JCSS, vol. 25(2), pp. 145–180, Oct. 1982
Hutchins E., Understanding Micronesian Navigation, Mental models, D. Gentner and A. L. Stevens, (Eds.), pp. 191–225, Lawrence Erlbaum Associates, 1983
Kaufmann A., M. M. Gupta, Introduction to Fuzzy Arithmetic: Theory and Applications, Van Nostrand Reinhold Co., New York, NY, 1985
Kuipers B. J., T. S. Levitt, Navigation and Mapping in Large-Scale Space, AI Magazine, 1988
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
Ladkin P., The completeness of a natural system for reasoning with time intervals, in Proc IJCAI, pp. 462–467, 1987
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
Malik J., T.O. Binford, Reasoning in time and space, in Proc IJCAI, pp. 343–345, W. Germany, 1983
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
McDermott D., A temporal logic for reasoning about processes and plans, Cognitive Science, vol. 6, pp. 101–155, 1982
McDermott D., A theory of metric spatial inference, In Proc. of AAAI, 1980
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
McDermott D., Ernest Davis, Planning and Executing Routes through Uncertain Territory, Artificial Intelligence, vol. 22, pp. 107–156, 1984
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
McReynolds J., Geographic Orientation of the Blind, Ph.D. dissertation in U.T., 1951
Montanari U., A note on minimal length polygon approximations, CACM, vol. 13, pp. 41–47, 1970
Moszkowski B. C., Executing temporal logic programs, Cambridge University Press, 1986
Piaget J., B. Inhelder, The Child's Perception of Space, Norton, New York, 1967
Pratt V. R., Process logic, In Proc. 6th POPL, pp. 93–100, ACM, Jan. 1979
Prior A. N., Past, present and future, Clarendon Press, Oxford, 1967
Rescher N., A. Urquhart, Temporal Logic, Springer Verlag, New York, 1971
Retz-Schmidt G., Various Views on Spatial Propositions, Al Magazine, vol. 9, Summer 1988
Segev A., A. Shoshani, Logical modeling of temporal data, in the Proc. of the ACM-SIGMOD International Conference on the Management of Data, 1987
Sheng R. L., A linguistic approach to temporal information analysis, Ph.D. thesis, UC, Berkeley, 1983
Shoham Y., Reasoning about change: Time and causation from the standpoint of artificial intelligence, MIT Press, Cambridge, MA, 1988
Snodgrass R., I. Ahn, A taxonomy of time in databases, In the Proc. of the ACM SIGMOD International Conference on Management of Data, 1985
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
Tsang E. P. K., Time structures for AI, Proceeding of the 10th IJCAI, 1987
Van Benthem J.F.A.K., The logic of time, D.Reidel, 1983
Vitek M., Fuzzy information and fuzzy time, Proc of IFAC, pp. 159–162, Marseille, France, 1983
Yager R.R., On different classes of linguistic variables defined via fuzzy subsets, Kybernetes, vol. 13, pp. 103–110, 1984.
Zadeh L. A., A computational approach to fuzzy quantifiers in natural languages, Computers and mathematics, vol. 9, pp. 149–184, 1983
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
Zadeh L. A., Fuzzy Sets, Information Control, vol. 8, pp. 338–353, 1965
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
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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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