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

 
   

14.6 Boundaries, Coincidence, and Adjacence

We do not consider boundaries as being parts of entities. The boundary-of relationship connects entities of various categories, namely (a) time-boundaries and chronoids, (b) spatial boundaries and space regions, (c) presentials and processes, and (d) material boundaries and material structures. We have not introduced a general relationship, but particular boundary-relations for each of these cases. Case (a) relies on the notions of left and right boundary-of, $\Glb(x,y)$ and $\Grb(x,y)$, respectively. In case (b), $\Gbd(x,y)$ denotes the fact that $x$ is a spatial boundary of $y$. Case (c) is discussed in the section on time and space, whereas the fourth case is not yet formalized.

Space and time entities with an extension allow for the notion of congruence, e.g. two topoids are congruent if they share exactly the same size and shape. The relation of congruence is mentioned in section 5.2.

Coincidence is a relationship between space boundaries or time boundaries, respectively. Intuitively, two such boundaries are coincident if and only if they occupy ``the same'' space, or point in time, but they are still different entities (cf. sect. 5). Obviously, congruence of extended boundaries like surfaces is entailed by their coincidence.

Further, the notion of coincidence allows for the definition of adjacency. In the case of space-time-entities, these are adjacent as soon as there are coincident parts of their boundaries. In contrast, material structures and processes cannot have coincident boundaries. Nevertheless, they are adjacent if the projections of their boundaries are adjacent.

Robert Hoehndorf 2006-10-18
 
       
     
     
     

   
     
     
       
 

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