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Spatial Representation and Reasoning in Artificial Intelligence

  • Laure Vieu
Chapter

Abstract

Space, like time, is one of the most fundamental categories of human cognition. It structures all our activities and relationships with the external world. It also structures many of our reasoning capabilities: it serves as the basis for many metaphors, including temporal, and gave rise to mathematics itself, geometry being the first formal system known.

Keywords

Spatial Representation Local Space Relative Space Spatial Reasoning Axiomatic Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. 1.
    The term relational is also found.Google Scholar
  2. 2.
    The domain can hold three types of entities — points, lines, and planes — with an incidence relation (not membership) between them. In Tarski (1959), an axiomatic system of Euclidean geometry based only on points is proposed; in this same system, continuity axioms are freed from any reference to arithmetic.Google Scholar
  3. 3.
    When transposed to AI, one can see reasoning in global spaces as model-based and reasoning in local spaces as deductive. However, model-based reasoning in global spaces is in general replaced by more efficient numerical algorithmic methods.Google Scholar
  4. 4.
    Defining “good” identity criteria is very difficult. Spatiotemporal continuity is, however, often adopted as one of these criteria, which in this case would make the definition of continuity of motion circular.Google Scholar
  5. 5.
    For a review of possible ways of defining points in terms of regions, see Gerla (1994).Google Scholar
  6. 6.
    When there are no boundaries (as, for instance, for the whole space), the subset is both open and closed.Google Scholar
  7. 7.
    For instance, in the standard topology of IR, IR2, or IR3, all open sets but the empty set are of the same dimensionality as the whole topological space.Google Scholar
  8. 8.
    In the TACITUS project (Hobbs et al., 1987; Hobbs et al., 1988), a point-based global space is proposed, with independent “scales” or granular partial order relations (one for each axis).Google Scholar
  9. 9.
    In all generality, the case A = 7r should be distinguished.Google Scholar
  10. 10.
    This means that these distance calculi require some underlying orientation system.Google Scholar
  11. 11.
    To restrict memory size, they are sometimes compacted and hierarchically organized, as in Samet (1984; 1989).Google Scholar
  12. 12.
    Regions extended throughout or, formally, regions x such that x = x and x=æ. Google Scholar
  13. 13.
    This way, a distinction can be made between jointing along a “fiat boundary” (Smith, 1995) (for example, the relation between two halves of a ball) and touching along real, objective, boundaries (for example, the relation between the ball and the ground).Google Scholar
  14. 14.
    Note that Clarke’s theory and RCC do not imply this last restriction.Google Scholar
  15. 15.
    One may question the cognitive or physical plausibility of these particular regions. Indeed, perfect spheres may be seen as entities as abstract as points. As a consequence, a region-based geometry relying on the existence of spheres may be no more attractive than a point-based geometry.Google Scholar
  16. 16.
    Except when there is a NTP relation between them or when they are equal, in which case orientation has no meaning. Notice that Hernandez assumes that a TPP relation can be combined with orientation, considering the position of the common boundary, thus forbidding this shared boundary to be very long or to be scattered around the regions.Google Scholar
  17. 17.
    This includes the case of the relation between one history and a static object, since immobility can be seen as being relative to a point of view.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1997

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  • Laure Vieu

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