


Overview
General Formal Ontology (GFO)

Subsections
14.5 Parthood Relation
Partof is a basic relation between certain kinds of entities, and
several relations have a similar character.
The abstract partof relation is denoted by , while
the argumenttypes of this relation are not specified, i.e., we allow
arbitrary entities to be arguments. We assume that satisfies
the condition of a partial ordering, i.e., the following axioms:
Domainspecific partofrelations are related to a particular
domain ,
which might be the set of instances of a category. We denote these
relations as
. We assume that for a domain ,
the entities of and its parts are determined. There is a large family
of domainspecific partof relations, the most general of these are related
to basic categories as , , ,
, , .
In the following sections we provide an overview of the most important
categoryspecific partof relations.
We hold that the partofrelation of sets is defined by the set inclusion,
hence
.
If we assume the powerset axiom for sets, then the mereology of sets
corresponds to the theory of Boolean algebras.
The partof relations of time and space are related to chronoids, timeregions,
topoids, and space regions. We introduce the unary predicates ,
, , , and the binary relations
, .
Every notion of partof allows for a nonreflexive version of the
relationship, which expresses proper parthood. These are denoted by adding a
``p'' to the above predicates, e.g.
or
.
In particular, applies to spatial regions, refers to
time regions and chronoids, while represents a relationship
between situoids (or situations) and their constituents. The
constituents of a situoid include, among
other entities, the pertinent material structures (that participate
in ) and the qualities that inhere in them. Further, facts and
configurations are constituents of situoids. Not every part
of a constituent of a situoid, however, is contained in it.
The basic relations pertaining to material structures are ,
for `` is a material structure'', and
, which means
that the material structure is a part of the material structure
. We assume among the basic axioms:
We stipulate that the relation
is a partial
ordering, but
additional axioms depend strongly on the domain under consideration.
The partof relation between processes is denoted by
,
meaning that the process is a processual part of the process
. We assume the basic axiom:
.
states that the process has the temporal
extension , or that the process is temporally projected onto .
Again, we stipulate that the relation
is a partial ordering,
but additional properties of this relation depend on a concrete domain.
For example, in the processes of surgery, only certain processual parts are
relevant.
The roleof relationship was
introduced as a close relative of partof. It relates
roles and their contexts , denoted by . Thus far
we have introduced roleof between processual roles and processes and
between relational roles and relators.
Robert Hoehndorf
20061018

