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A representation for modeling functional knowledge in geometric structures

  • Amitabha Mukerjee
Knowledge Representation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 444)

Abstract

Most geometric models are quantitative (half-spaces and transformations), making it difficult to perform the kind of abstraction needed to model the underlying functional knowledge. Typically, users have used ad hoc subjective notions to perform this abstraction, which we call the "get-beneath-the-geometry" syndrome.

In this work we describe a systematic representation scheme that builds spatial maps based on local relations between objects. It derives relations that are more "functionally relevant" - i.e. those that involve accidental alignments, or can be described based on such alignments. The principal advantages of this representation in building functional descriptions is that
  1. a)

    it is free of subjective bias,

     
  2. b)

    it is complete in the qualitative sense of distinguishing all overlap/tangency/nocontact geometries.

     

In addition, the model is capable of handling uncertainty in the initial system (e.g. "the fuse box is somewhere behind the compressor") by constructing bounded inferences from disjunctive input data. Two kinds of uncertainty can be handled — those arising from deliberate imprecision in the interest of compactness ("down the road from"), or those caused by an inadequacy of data (sensors, spatial descriptions, or maps).

The representation is an extension to two and higher dimensions of the one-dimensional interval logic [Allen 83]. In orthogonal domains, this extension is straightforward, but a new non-commutative algebra has been developed for handling angular relations.

Keywords

Spatial reasoning path planning knowledge representation natural language generation 

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References

  1. [Allen 83]
    Allen, James F., Maintaining knowledge about temporal intervals, Communications of the ACM, vol.26(11), November 1983, pp.832–843.Google Scholar
  2. [Ambler and Popplestone 75]
    Ambler, A.P., and R.J. Popplestone, Inferring the positions of bodies from specified spatial relations, Artificial Intelligence, v.6:129–156.Google Scholar
  3. [Chang and Jungert 86]
    Chang, S.K., and Jungert E., A spatial knowledge structure for image information systems using symbolic projections, IEEE Fall Joint Computer Conference, 1986, pp. 79–86.Google Scholar
  4. [Dennett 75]
    Dennett, David C., Spatial and temporal uses of english prepositions — an essay in stratificational semantics, Longman Group, London 1975.Google Scholar
  5. [Peuquet and Ci-Xiang 87]
    Peuquet, Donna J., and Zhan Ci-Xiang, An algorithm to determine the directional relationship between arbitrarily-shaped polygons in the plane, Pattern Recognition, v.20(1):65–74, 1987.Google Scholar
  6. [Mukerjee and Joe 89]
    Mukerjee, Amitabha, and Joe, Gene, Representing spatial relations between arbitrarily oriented objects, Proceedings of the Second International Conference on Machine Intelligence and Vision (MIV-89), Tokyo, April 1989, p. 288–291. (also available TR 89-017 from Texas A&M University, Department of Computer Science).Google Scholar
  7. [McCarthy 77]
    McCarthy, John, Epistemological problems of artificial intelligence, Proceedings IJCAI-77, Cambridge MA, 1977, p.1038–1044.Google Scholar
  8. [Retz-Schmidt 88]
    Retz-Schmidt, Gudula, 1988. Various views on spatial prepositions, AI Magazine, Summer 1988, p. 95–105.Google Scholar
  9. [Winston 75]
    Winston, Patrick Henry, 1975. Learning structural descriptions from examples, The Psychology of Computer Vision, ed. Patrick Henry Winston, McGrawHill, 1975, p.157–209. (Also reprinted in "Readings in knowledge representation", ed. Ronald J. Brachman and Hector J. Levesque, Morgan Kaufman, 1985).Google Scholar
  10. [Requicha 80]
    Requicha, A.A.G., Representation for Rigid solids: Theory, methods, and systems, ACM Computer Surveys, Dec. 1980.Google Scholar
  11. [Shepard 80]
    Shepard, R.N., Multidimensional scaling, tree-fitting and clustering, Science, vol.230, pp.390–398.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Amitabha Mukerjee
    • 1
  1. 1.Department of Computer ScienceTexas A&M UniversityUSA

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