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Onto-Med >> Theories >> GFO Part I Basic Principles

 
   


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 point-like time-boundaries: Boundaries of regions are surfaces, boundaries of surfaces are lines, and boundaries of lines are points. As in the case of time-boundaries, 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 $t$, we may introduce a universal $U(t)$ whose instances are topoids that are congruent with $t$.

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 ending-point of the first object and (c) a true starting-point 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 2006-10-18
 
       
     
     
     

   
     
     
       
 

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