General Formal Ontology (GFO)
7.1 Material Structures, Space, and Time
A material structure is a presential; hence, it exists at a time-point
, denoted by . Furthermore, a material structure exhibits
the ability to occupy space.
This ability is based on an intrinsic quality of ,
which is called its extension space or inner space.
The relation defines the condition that is the extension
space of , and the extension space is regarded a quality similar to
its weight or size.
Every material structure occupies a certain space-region that exhibits
the basic relation of to space. The relation
describes the condition that the material structure
occupies the space-region . A material structure is spatially
contained in the space-region , if the space-region occupied by , is
a spatial part of . In this case we say that is the spatial location
of with respect to . The relation depends on granularity;
a material structure , for example, may occupy the mereological
sum of the space-regions occupied by its atoms or the convex closure
of this system. We assume that in our considerations the granularity
is fixed, and - based on this dimension - that the
space-region occupied by a material structure is uniquely determined.
For , we may ask whether for every spatial part of there
exists a uniquely determined material structure that occupies . In
this case is called a material part of ; this relation is
. Such a strong condition is debatable because it
might be that the substrate that a material structure comprises has
non-divisable atoms. For this reason we introduce the
as a new basic relation, and stipulate the axiom
implies that the region occupied by is a spatial
part of the region occupied by .
granularity plays a role here, we separately stipulate to this condition for every
fixed occupation-relation separately.
A spatial region
frames a material structure
if the location that occupies is a spatial part of .
Material structures may be classified with
respect to the mereotopological properties of their occupied space
regions. A material structure is said to be
connected if its occupied
region is a topoid.