Topological Constraints: A Representational Framework For Approximate Spatial And Temporal Reasoning

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.

[1]  Didier Dubois,et al.  Processing fuzzy temporal knowledge , 1989, IEEE Trans. Syst. Man Cybern..

[2]  Henri Prade,et al.  Uncertainty Handling and Fuzzy Logic Control in Navigation Problems , 1986, IAS.

[3]  Drew McDermott,et al.  Planning Routes Through Uncertain Territory , 1983, Artif. Intell..

[4]  Peter B. Ladkin,et al.  The Completeness of a Natural System for Reasoning with Time Intervals , 1987, IJCAI.

[5]  Zohar Manna,et al.  A Hardware Semantics Based on Temporal Intervals , 1983, ICALP.

[6]  Ronald R. Yager,et al.  ON DIFFERENT CLASSES OF LINGUISTIC VARIABLES DEFINED VIA FUZZY SUBSETS , 1984 .

[7]  M. Vitek Fuzzy Information and Fuzzy Time , 1983 .

[8]  James F. Allen Maintaining knowledge about temporal intervals , 1983, CACM.

[9]  Y. Shoham Reasoning About Change: Time and Causation from the Standpoint of Artificial Intelligence , 1987 .

[10]  D. McDermott A Temporal Logic for Reasoning About Processes and Plans , 1982, Cogn. Sci..

[11]  Soumitra Dutta,et al.  Qualitative Spatial Reasoning: A Semi-quantitative Approach Using Fuzzy Logic , 1989, SSD.

[12]  Ben C. Moszkowski,et al.  Executing temporal logic programs , 1986, Seminar on Concurrency.

[13]  Drew McDermott A Theory of Metric Spatial Inference , 1980, AAAI.

[14]  Edward P. K. Tsang,et al.  Time Structures for AI , 1987, IJCAI.

[15]  Richard T. Snodgrass,et al.  A taxonomy of time databases , 1985, SIGMOD Conference.

[16]  Alberto Elfes,et al.  Using occupancy grids for mobile robot perception and navigation , 1989, Computer.

[17]  Richard T. Snodgrass,et al.  The temporal query language TQuel , 1987, TODS.

[18]  L. Zadeh A COMPUTATIONAL APPROACH TO FUZZY QUANTIFIERS IN NATURAL LANGUAGES , 1983 .

[19]  A. Kaufmann,et al.  Introduction to fuzzy arithmetic : theory and applications , 1986 .

[20]  Z. Manna,et al.  Verification of concurrent programs: a temporal proof system , 1983 .

[21]  Takeo Kanade,et al.  Intelligent Autonomous Systems , 1991, Robotics Auton. Syst..

[22]  Brian R. Gaines,et al.  Foundations of fuzzy reasoning , 1976 .

[23]  R. Sheng A linguistic approach to temporal information analysis , 1984 .

[24]  Johan van Benthem,et al.  The Logic of Time , 1983 .

[25]  Vaughan R. Pratt,et al.  Process logic: preliminary report , 1979, POPL.

[26]  Shashi K. Gadia Toward a multihomogeheous model for a temporal database , 1986, 1986 IEEE Second International Conference on Data Engineering.

[27]  Herbert Freeman,et al.  Computer Processing of Line-Drawing Images , 1974, CSUR.

[28]  David Harel,et al.  Process logic: Expressiveness, decidability, completeness , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[29]  Benjamin Kuipers,et al.  Navigation and Mapping in Large Scale Space , 1988, AI Mag..

[30]  Jitendra Malik,et al.  Reasoning in Time and Space , 1983, IJCAI.

[31]  Ugo Montanari,et al.  A note on minimal length polygonal approximation to a digitized contour , 1970, CACM.

[32]  Didier Dubois,et al.  Possibility Theory - An Approach to Computerized Processing of Uncertainty , 1988 .

[33]  Alasdair Urquhart,et al.  Temporal Logic , 1971 .

[34]  Arie Shoshani,et al.  Logical modeling of temporal data , 1987, SIGMOD '87.

[35]  S. Dutta,et al.  An event based fuzzy temporal logic , 1988, [1988] Proceedings. The Eighteenth International Symposium on Multiple-Valued Logic.

[36]  Dana H. Ballard,et al.  Strip trees: a hierarchical representation for curves , 1981, CACM.

[37]  Richard T. Snodgrass,et al.  Extending the relational algebra to support transaction time , 1987, SIGMOD '87.

[38]  Lotfi A. Zadeh,et al.  A Theory of Approximate Reasoning , 1979 .