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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.

@TechReport{,
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:

- 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]

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

- represent imprecise relationships (e.g. "I'm sitting in
the railway station")
- can handle uncertainty (e.g. you don't know the spatial
relationship between two objects)
- Granularity depends on context (e.g. the distances
referred to in "the moon rises over a field" and "a bridge
over water" are different.)

Ontology of relations between two objects (each has a converse,
forming 8 relations) one-dimensionally:
- a is left of b
- a is attached to b
- a is overlaping b
- a is inside of b

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]:

- compute composition of spatial relations
- use constraint satisfaction to remove inconsistencies

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:

- The third constraint (granularity) is related to viewing
things at multiple levels of abstraction.
- This notion of spatial reasoning does not include adding
objects to the image, which makes it limited for problem solving.

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