General Formal Ontology (GFO)
The following example is discussed in (39),
for the DOLCE and other approaches therein. We
refer to the formalization in the framework of DOLCE only.
A formalization in GFO is expounded and then compared to the DOLCE
The example is stated as follows in (39):
``A statue of clay exists for a period of time going from
to . Between and , the statue is crashed
and so ceases to exist although the clay is still there.''
Many entities can be identified on the basis of the
statement. The term ``statue'' may have different meanings; we assume
that ``statue'' denotes a persistant of material
objects, with a certain lifetime
, which we assume to be a
chronoid. ``clay'' is an amount of substrate . The statue
consists of the
amount of clay . More precisely, at each
time-boundary at which a presential instantiates the
, there is a presential amount of substrate of which the
instance of consists:
The demolition is a process , in
which many different (sub-)processes and material structures may be
involved. The demolition is projected onto a
framing chronoid, say
, with starting time-boundary , and ending
The original statement refers to three time-boundaries, , , and
, and the following ordering holds among them:
29. The statue exists from
to , thus one can assume that
starts with , therefore . We may further expect
that at , the statue is present, but at
, the statue ceased to exist. Further,
participates in the beginning of the demolition,
in the whole event.
The lifetime of and the framing chronoid
overlap, more exactly there is a chronoid , such that is an
end-segment of and at the same time an initial segment of
The process-boundary at does not contain a constituent part that is
an instance of the persistant , but there is a material
structure which is the ``successor'' of , in the sense
that its instances are ontically connected with those of :
Finally, let us consider the point in time when the
statue ceases to exist. This can be understood as an extrinsic change,
such that before the change, still persists, whereas
after the change, it does not:
Figure 2 provides a graphical overview
of some connections between the aforementioned entities.
Visualization of some aspects of the formalization
We consider to refer to time-boundaries,
which is not possible in DOLCE, because it does not have this notion of
However, we consider time-boundaries more adequate, based on the
expressions ``going from to '' and
``between and ''. Altogether, relating the entities to
time (and space) is different in DOLCE as compared with GFO, because there is
no direct projection (e.g. ), but DOLCE establishes the link to
time and space as a relation to qualities.
Similarly, on the basis of time-boundaries, GFO can formalize the
extrinsic change covering the particular moment when the statue is no
longer considered as existent. Note that this depends on the
granularity of the model, while the granularity is not yet
explicitly expressible in GFO.
The remainder of the formalization appears rather similar to that of
DOLCE. The relationship between the statue and the clay
is covered ( in DOLCE, in GFO), but note that this relation
will be extended and revised in terms of the theory of levels,
cf. sect. 4. The participation of the statue and the
clay in the demolition are expressed in DOLCE (by ) and GFO as well
( and ).
This example will provide a rough overview of the
GFO ontology in a single, coherent, (but rather simple) modeling
case. It employs many, yet not all applicable GFO categories.
Let us consider a 100-metre sprint, in which two runners take part:
and . The race starts with the signal at time
and lasts until , when the last runner crosses the
quickly reaches a high speed and takes the first
position, while does not accelerate that rapidly but
manages to pass at . At ,
crosses the finishing line, winning the race. The victory
of is a big surprise for the audience, so the race
is broadly discussed and is announced to be the most surprising and
interesting race of the decade.
For brevity, let and
The whole race can be interpreted as one complex
entity extended in time, namely a situoid , spatially delimited
by a topoid :
, and temporally framed by a chronoid :
. is associated with certain universals, which
select the point of view and granularity. Here we assume that these
universals are , and , which
delimit the context in which we analyze the race. So, we have
have identified the chronoid , framing the
race. It has a left boundary as the race starts,
, and a right boundary
, where crosses the finish line, .
Moreover, we identify two inner boundaries,
, that are of special
interest: , where takes the lead and where he
wins the race.
The persistence of the runners
throughout the entire race is provided by viewing them as two persistants,
, which are instantiated by ontically
connected presentials present at each time boundary of
the race. Each persistant persists through
time, or more precisely, through the time boundaries on which its
instances exist. Moreover, each persistant participates in
the process of the race. Analogous considerations
apply to the persistence of the audience and the track.
The location of
the race is determined by the topoid
framing the situoid . The
topoid is assumed to be a convex closure of the
mereological sum of all space regions occupied by the material
structures constituting the situations of . In our
case, is the sum of space regions of the presential runners, the track
and the audience, across the overall period of the race.
At each time boundary in the course of the
race, one can project the race to its boundaries , which are
situations. In particular, one may consider the situations at
which are referred to in the example. Each of these situations is a
compound of several constituents, of which those are of particular
interest. They are determined by the universals associated with
the situoid race.
Therefore, we focus on
All constituents of the
situations of the race considered here are material structures, and as
such occupy some spatial region (cf. the remarks on space regions and
topoids above), and consist of some presential amount of
substrate. For example, we could say that is a solid substrate
of the runner:
Moreover, each material structure comes
together with its individual properties. The runners or the track,
for example, inhere qualities like speed, blood pressure or
hardness (here: of the track). In the case of the property universal
, for example, at each time boundary of the race we
find an individual speed for each runner, as well as individual values
of those property individuals: let the speeds of the runners at be
25km/h and 30mph, respectively. We observe that the
individual property values are instances of the categorial property
values belonging to two different measurement systems. The first measurement system is a set of values in the
form of pairs of a number and the unit ``km/h'', while the second is a
set of values with unit ``mph''. Nevertheless, the individual
quality values 25km/h and 30mph are comparable, since the
individual qualities they refer to, say
instances of the same property speed.
Further, one can find properties of the whole race, which seem to be
indicated by the expression: ``it was the most surprising and
interesting race of the decade''. Here we identify
being-the-most-interesting-race-of-decade as the quality
value of the individual quality,
level-of-entertainment-of-the-race. It is clear, however, that this
quality does not belong to the material, but rather to the social
level. Here we do not say it inheres in .
The race as a process is a combination of several
processes, among them
processes. Here we can observe
that either of these processes is a coherent process, the
boundaries of which contain material structures, namely instances of
the persistants referred to above, . Hence, we have
, and all of those instances
are ontically connected (for the same ).
Moreover, we observe certain dynamics between those
processes, which can be modelled using intrinsic and extrinsic
changes. First, the changes in the speed of the runners can be
interpreted as intrinsic changes. Second, we may identify an
extrinsic change at , when takes the lead. To represent this change we identify
two parts of the process , namely
These processes meet at which means that
and a coincident time-boundary are the pair of
the right boundary of the projection of
and the left boundary of the
. The extrinsic change of taking the lead - or
switching from the position of losing the race to the position of
winning - by is represented as change(
), with and representing the process
boundaries at the end and at the beginning of
, respectively. Analogously, the crossing of the
finish line by the could be represented, which is a
change from winning to being the actual winner.
So far we have concentrated on the material aspects
of the race, where runners are identified as material objects with
inherent material qualities. But we should keep in mind that the
runners and the race cannot be reduced to the movement of two material
objects along the line of the track. Rather we identify runners as
the social roles of some individuals, just as the track is the
role of some solid object of a certain shape with certain properties. We
see that the situoid , in part, does not belong
to the material level, but to the
social and conceptuals level as well. At the social
level, we do not consider bodies with material
qualities, but rather social objects, their roles, e.g. being runners
or the audience, and their social qualities, together with their
corresponding values, like those of winning or losing.
This example is taken from the domain of clinical trials, one of the
major fields for application of the research group Onto-Med. The example
is a first attempt to define the term ``staging''
using GFO, and illustrates the method for ontological
mappings, cf. sect. 2.4.
There are various sources for defining staging, including
discussions with medical experts. Therefore, we provide our own
definition, based on discussions with our medical experts,
respective literature, e.g. ``Pschyrembel'' (47) and
and several websites31.
The definition is divided into three parts of overall validity, some
background facts of frequent validity and general background
Staging is a process composed of the detection of
the anatomic extent of tumor32 and the classification of the result
with respect to a staging system.
Anatomic extent refers to the
size of the tumor, in both its primary location and in metastatic
sites. The most common staging system is the TNM classification, but
there are others, e.g. those used for cancers of children and those
used for cancers of female
reproductive organs. Staging is applied to malignant tumors. The
result of staging, i.e., the classification in a staging system, is
used for treatment planning, prognosis evaluation and the comparison
There are four types of staging. Clinical-diagnostic staging
involves what a doctor can see, feel and determine through x-rays and
other tests. Surgical-evaluative staging involves exploratory
surgery, biopsy or both. After surgery, the tumor can be
directly examined and its cells microscopically analysed, which is
called post-surgical-treatment pathologic staging. If
additional or new treatments are applied to the same disease,
re-treatment staging uncovers the extent of the tumor.
A tumor is a disease that
causes the growth of tumor (often tumor tissue).
Following the axiomatic method, we begin by collecting important
terms from their definitions. There are: staging, process, detection,
anatomic extent, tumor, classification, staging system, disease,
tumor, primary location, metastatic site, size and malignant.
Now these terms can be analyzed and ontologically embedded into GFO.
Each term is subsumed by a GFO category or linked to GFO
categories by means of basic relations, as specifically as possible. We
analyze and group terms with respect to the basic category to which
Staging is a process that is composed of two
steps, a process of detection and a process of classification. Thus,
staging is a discrete process. Detection and classification are
processes as well, but they are not analyzed in detail here, since
they will be used as domain primitives below. Further, each disease is
a process, and thus a tumor, as well.
Topoids are only indirectly involved, through the notions of
``location'' and ``site''. These refer to topoids determined relative
to the body of the patient and the tumor, respectively. A
tumor may spread throughout the body. The topoid occupied by that
part of the tumor first occurring or discovered is called the
primary location. Topoids of other tumor parts (metastases) are
called metastatic sites.
Consider the anatomic extent of the tumor,
which is determined and classified during staging. This should be
understood as a situation rather than a single quality, although the
latter may appear appropriate at first glance. This situation refers
to (a) the size of the parts of the tumor at the primary location
and metastatic sites, (b) the relationship between the tumor, the
involved anatomic entity and adjacent anatomic entities, and (c)
possibly more relations between the tumor and the body
(cf. the TNM staging system).
sizes of connected parts of the tumor are qualities that are
measured in centimeters or inches. Second, there is an evaluative
quality of a tumor, which is the degree of malignity. The simplest
measurement system contains just the values
``malignant'' and ``benign'', which are mutually exclusive. Usually,
malignant tumors are staged.
A tumor (often tumor tissue) is a
material structure, which is created and (usually) growing throughout the
course of the disease, i.e., tumor.
In order to fully describe the notion of a staging
system, the category of symbolic structures
is required. A staging system is, in the simplest case, a set of
symbolic structures that denote universals of anatomic extents
(viewing the extent of a tumor as a multi-dimensional or
-faceted configuration, as introduced above).
However, this cannot be further analyzed without a deeper understanding
of symbolic structures and the denotation
The above descriptions provide an ontological embedding of several
domain-specific terms into GFO. However, this is obviously rather
weak, e.g. for staging only, a structural decomposition into two
processes could be stated. In order to add domain-specific
dependencies, a domain extension is necessary. That means, new
primitives must be added and ontologically embedded, which can then be
used to express more domain-specific interdependences.