General Formal Ontology (GFO)
14.5 Parthood Relation
Part-of is a basic relation between certain kinds of entities, and
several relations have a similar character.
The abstract part-of relation is denoted by , while
the argument-types 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:
Domain-specific part-of-relations are related to a particular
which might be the set of instances of a category. We denote these
. We assume that for a domain ,
the entities of and its parts are determined. There is a large family
of domain-specific part-of relations, the most general of these are related
to basic categories as , , ,
, , .
In the following sections we provide an overview of the most important
category-specific part-of relations.
We hold that the part-of-relation of sets is defined by the set inclusion,
If we assume the power-set axiom for sets, then the mereology of sets
corresponds to the theory of Boolean algebras.
The part-of relations of time and space are related to chronoids, time-regions,
topoids, and space regions. We introduce the unary predicates ,
, , , and the binary relations
Every notion of part-of allows for a non-reflexive version of the
relationship, which expresses proper parthood. These are denoted by adding a
``p'' to the above predicates, e.g.
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
additional axioms depend strongly on the domain under consideration.
The part-of 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
The role-of relationship was
introduced as a close relative of part-of. It relates
roles and their contexts , denoted by . Thus far
we have introduced role-of between processual roles and processes and
between relational roles and relators.