General Formal Ontology (GFO)
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
respectively. In case (b), denotes the fact that
is a spatial boundary of . 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.