Part-whole example for how-to-do document

Here is my part-whole example for the how-to-do document.  This is
in the form of a general how-to-do guide for expressing part-whole
relations in OWL, and includes a discussion of some of the issues
(with some valuable input from Guus).

I plan to include Guus's wine-region example as part of this section
of the document.  If anyone has any other part-whole examples,
please send them to me, and I'll include them in the write-up, when I
add Guus's.




Although part-whole relations play an central role in many domains,
there is no consensus on how part-whole relations should be modeled.
Of course, everyone agrees that part-whole relations should not be
mixed with the kind-of (subsumption) hierarchy.  Although this
may seem obvious to those familiar with ontologies, there are examples
where this still occurs -- e.g., some controlled medical terminologies.
Beyond this, there is one principle that is generally accepted:  the
part-whole relation is a transitive relationship.  One can infer,
for example, that since the finger is part of the hand and the hand
is part of the human body, then the finger is part of the human body.

On the surface, however, it appears that transitivity does not always
hold.  The classic example is the following:  an arm is part of a musician,
the musician is part of an orchestra, but it would be odd to conclude
that the arm is part of the orchestra.  However, this example is not
completely convincing, since an arm is not part of a musician per se,
but of a human (body).  "Musician" is a role of a human.

A more convincing example is provided by Rogers and Rector:  a part-of
an artery is part-of the thigh, and the thigh is part-of the leg, but a
part-of an artery is not normally thought of as part-of the leg.  Many
authors (including Rogers and Rector) have argued that the solution to
such examples is to distinguish different kinds of part-whole relations,
and then to not mix them.  Winston, Chaffin and Herrmann, for example,
proposed six different types of part-whole relations (specializations):
(1) component-integral_object
(2) member-collection
(3) portion-mass
(4) stuff-object
(5) feature-activity
(6) place-area.

Rogers and Rector block the a-part-of-an-artery-is-part-of-the-leg inference
by distinguishing two specializations:  segment-of and component-of.  (Rogers
and Rector treat "segment-of" as a subspecialization of the portion-mass
specialization.)  Thus, a segment-of an artery is a component-of the thigh,
and the thigh is a segment-of the leg, but a segment-of an artery is not a
segment-of the leg.  The inference is blocked by not allowing transitivity
across two different specializations of part-whole.  Although most authors
agree that something like this notion of part-whole specialization is needed,
there is no agreement as to what the specialization categories should be.

It should be pointed out that sometimes transitivity can lead to
examples that seem linguisticly odd, even though they are confined to
a part-whole specialization and are conceptually correct.  For example,
a fingernail is part of the finger, which is part of a hand, which is
part of an arm, although it does seem somewhat odd to say that a
fingernail is part of an arm.  Part of the problem here is that what
we mean by "arm" is somewhat ambiguous.  We may mean the extremity
attached to the shoulder, or we may mean the extremity between the
shoulder and the hand.

In light of this overview, one can conclude that part-whole
relationships can be safely modeled if the following three
principles are followed:
(1) Keep kind-of and part-of hierarchies strictly separate.
(2) Treat part-of as a transitive relation (i.e., a property that
    is transitive).
(3) Create specialized part-of relations to reflect different uses
    of part-of, allowing transitivity only within a specialization.

Finally, it should be noted that although following these principles
should  lead to a model that doesn't make any false inferences, it
will not necessarily allow all the inferences that one may ideally
want to model.  In particular, fully modeled part-of relations
may need to allow limited inheritance of certain properties --
whereas a model based on the above principles will not.  For
example, in some domains such as human anatomy, functions of some
substructures may be inheritable via the component-of relation, but
only up to a certain level:  The Islets of Langerhans are components
of the pancreas and they are what secrete insulin; yet, we
attribute this function to the whole pancreas, although we don't
carry this attribution to the gastrointestinal system (Rogers
and Rector).

Inheritance (or propagation) in part-whole relationships is very
complex.  There can be standard inheritance (like with subclass) --
e.g., the owner of the whole is also owner of the part.  There can be
upward propagation -- e.g., if the part if faulty, the whole is faulty.
And there can be systematic relationships -- e.g., the weight of the
whole is the sum of the weight of its parts.  Modeling such sophisticated
part-whole relationships is very difficult, and is beyond the scope of
this document.


As an illustration of how to model part-of relations in OWL, let
us start with the component-of specialization of the part-whole
relationship.  We will specify that all the classes of things that
are to be related in this way are subclasses of the Component class.
(This is a very flat class.  They may also be subclasses of other
classes that have more structure.)  The purpose of making them
subclasses of Component is to enable us to specify what kinds of
things can be related via the component-of relation.  For example,
in a human anatomy ontology, the class Heart would be declared to
be a subclass of both the class Organ and the class Component.  The
Component class would have the properties hasComponent and componentOf,
which are then inherited by Heart.  The AorticValve would also be
declared to be a subclass of the class Component as well as the
HeartValve class, which in turn is a subclass of Organ.  Then AorticValve
would be linked via the property componentOf to Heart.  The class
AorticValveCusp would be declared to be a subclass of Component and
Organ and linked via the property componentOf to AorticValve.
Because the property componentOf is transitive, one would be able
to infer that the AorticValveCusp is a component-of the Heart.

Since there may be other specializations of part-whole in which we
are interested, we make the component-of specialization a subproperty
of a general part-of property.  However, since we don't want transitivity
to carry over to other specializations, we specify that the subproperty
is transitive, not its parent property.  (This is different from the
wine-region example where we want transitivity across different types
of subareas, each of which is a subproperty.)

Below is a general scheme for modeling the component-of
relationship for any kind of component, be they parts of the
body or mechanical widgets.  The only aspect not discussed so
far is the class IntegralWhole.  In the human anatomy ontology,
the HumanBody class would be a subclass of the IntegralWhole
class since it would not have any componentOf property, but only
the hasComponent property.


widget:Component     rdf:type rdfs:Class.
widget:IntegralWhole rdf:type rdfs:Class.


widget:hasPart       rdf:type            rdfs:Property.
widget:PartOf        owl:inverseOf       widget:hasPart

widget:hasComponent  rdf:SubPropertyOf   widget:hasPart
widget:hasComponent  rdf:type            rdfs:TransitiveProperty.
widget:hasComponent  owl:allValuesFrom widget:Component.
widget:componentOf   owl:inverseOf     widget:hasComponent.
widget:componentOf   owl:allValuesFrom widget:Component widget:IntegralWhole.
widget:componentOf   owl:cardinality 1.


Winston, Chaffin and Herrmann.  A Taxonomy of Part-Whole Relations.
Cognitive Science, 11: 417-444, 1987.  [Seminal article on part-whole

Artale, A, Franconi, E., Guarino, N. and Luca, P.  Part-Whole
Relations in Object-Centered Systems:  An Overview.  Data and
KnowledgeEngineering 20(3): 347-383, 1966.
[Good overview of various approaches to part-whole relations]

Rogers, Jeremy and Rector, Alan.  GALEN's Model of Parts and Wholes:
Experience and Comparisions. <>
[Description logic based approach to part-whole relations.]

Schulz, S., Romacker, M. and Hahn, U..  Part-Whole Reasoning in
Medical Ontologies Revisited.  <>
[Another description logic based approach to part-whole relations]

Philips Research USA
**My opinions do not reflect those of my employer**

Received on Wednesday, 11 September 2002 16:40:23 UTC