


Overview
General Formal Ontology (GFO)

7.1 Material Structures, Space, and Time
A material structure is a presential; hence, it exists at a timepoint
, 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 spaceregion that exhibits
the basic relation of to space. The relation
describes the condition that the material structure
occupies the spaceregion . A material structure is spatially
contained in the spaceregion , if the spaceregion 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 spaceregions 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
spaceregion 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
denoted as
. Such a strong condition is debatable because it
might be that the substrate that a material structure comprises has
nondivisable atoms. For this reason we introduce the
relation
as a new basic relation, and stipulate the axiom
that
implies that the region occupied by is a spatial
part of the region occupied by .
Because
granularity plays a role here, we separately stipulate to this condition for every
fixed occupationrelation 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.
Robert Hoehndorf
20061018

