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Guesgen, H. W. (1989). Spatial reasoning based on Allen's temporal logic. International Computer Science Institute technical report. TR-89-049. 1947 Center St, Suite 600, Berkeley, CA.

  author =       {Hans Werner Guesgen},
  title =        {Spatial reasoning based on Allen's temporal logic},
  institution =  {International Computer Science Institute},
  year =         {1989},
  OPTnumber =    {TR-89-049},
  OPTaddress =   {1947 Center St, Suite 600, Berkeley, CA},

Author of the summary: Jim Davies, 2003, jim@jimdavies.org

Cite this paper for:

This work presents a cognitive model for qualitative spatial reasoning based on temporal reasoning suggested by J. F. Allen (1983).


Ontology of relations between two objects (each has a converse, forming 8 relations) one-dimensionally: The above ontology is inspired by Allen's relational ontology of 13 time relations between two intervals. [3] Certain relations are not captured by this (e.g. Jim is very far away from Jill) but the discussion will be limited to these 8 for clearness in this paper. [4]

It's reprensented with circular nodes (for objects) and rectangular labels (for relations). Spatial reasoning, on this count, is modifying the labels and inserting new rectangles.

Reasoning steps [6]:

Consider that there are rectangles between every pair of entities, each with each relation in them. reasoning, then, is culling the inconsistent ones. A transitivity table in the paper defines constraints that must hold in a network of spatial relations (again, similar to Allen's work).

Moving on two 2 and 3d

"Each quantitative relation can be uniquely mapped to a qualitative one, while in general there are in infinite number of quantitative relations that correspond to a qualitative one." [7]

To get to three dimensions, one can simply use three relations per pair of objects, each with respect to the x, y, and z axis. [10] The disadvantage is that certain ambiguities cannot be expressed tightly enough. Solving this problem by using sets of tuples improves it on this count, at the cost of a cubic disimprovement to the algorithm efficiency.

Summary author's notes:

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