


Overview
General Formal Ontology (GFO)

5.2 Space
Analogously to chronoids and time boundaries, the GFO theory of space
introduces topoids with spatial boundaries
that can coincide. Space regions are
mereological sums of topoids.^{12}
This approach may be called Brentano
space, and it is important to understand,
that despite the similarity between the basic time and space entities,
spatial boundaries can be found in a greater variety than pointlike
timeboundaries: Boundaries of regions are surfaces,
boundaries of surfaces are lines, and boundaries of lines
are points. As in the case of timeboundaries, spatial
boundaries have no independent existence, i.e., they depend on the
spatial entity of which they are boundaries.
To describe the form of an object, we adopt the relation of
congruence between topoids, that means ``two
topoids are congruent if they have the same shape and size.'' For
every topoid , we may introduce a universal whose instances are
topoids that are congruent with .
Similar to the problem of meeting processes, our approach with
coinciding boundaries of topoids is useful in modeling two objects
that are ``right next to'' each other (``touching''),
i.e., with (a) no gap between them, (b) a true endingpoint of the
first object and (c) a true startingpoint of the second. Again, a
model using real numbers as representation of spatial entities must
use either two closed, one open and one closed, or two open intervals
of real numbers. And just as in the temporal case, this violates at least one of the
conditions (a), (b) and (c).
Robert Hoehndorf
20061018

