General Formal Ontology (GFO)
Concrete individuals have a relation to time or space.
Material structures are presentials, hence they exists at a time-point, and
the relations captures this relation. The relation is
functional, hence a presential cannot exist at two different time-points.
The binary relation of occupation,
, describes a
fundamental relation between material structures and space regions.
Occupation is a functional relation because
it relates an individual to the minimal topoid in which a material
structure is located. Location is a less detailed notion,
which can be derived in terms of occupation and spatial part-of. An
is located in a region , , iff the topoid ,
occupied by , is a spatial part of .
Every process has a temporal extension. This temporal extension is called
the projection of the process to time, and is denoted by .
We distinguish several cases:
, , , where is a process, is
a presential, is
a chronoid, and is a time-boundary. The binary relations assign
a temporal entity to presentials and processes, while is
the projection of a process to its boundary , which is determined by
the time-boundary . Note that can be used to define the relations
Every situoid, for example the fall of a book from a desk, occurs over
time and occupies a certain
space. The binary relations of
framing, such as
binds chronoids or topoids to situoids . We
presume that every situoid is framed by exactly one chronoid and one
topoid. The relation
is to be read:
``the chronoid / topoid frames the situoid ''.