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10.4.4.5.2 Part-Whole Relations
There are a number of design issues that should be taken into account when model-
ing mereology (part-whole relations), many of which might be encountered in GI
ontologies. First, we should note that the two basic relationships hasPart and isPartOf
are inverses of each other. On an individual level, with individuals I1 and I2, if we
state that “I1 hasPart I2” and that isPartOf is the inverse of hasPart, then we know
that “I2 isPartOf I1.” However, this reciprocal inference does not hold at the class
level. For classes A and B, the statement “Every A hasPart some B” and isPartOf
is the inverse of hasPart does not allow us to assume that “Every B isPartOf some
A”; rather it must be stated explicitly, which adds a lot to the reasoner's workload.
Usually, it is best to decide to use either isPartOf or hasPart, depending on how the
ontology will be used and what the competency questions are.
In traditional mereology, the partOf relation is transitive, reflexive, and antisym-
metric. The antisymmetric property means that “Nothing is a part of its parts” (recall
that this is slightly different from asymmetry, which states that if A is related to B,
then B cannot be related to A). However, antisymmetry cannot be represented in
OWL 2. In mereology, since everything is a part of itself (reflexive), we need to add
in the term “hasProperPart” to deal with every part except the whole. In modeling,
one also needs to be careful that isPartOf is used only when it is really meant. Some
relationships that can be confused with mereological ones include
• Subclass (“is a kind of”)
For those used to modeling vocabularies, the superclass/subclass hierar-
chy is the only relationship on offer and is hence overused when in fact a
different, more meaningful relationship, such as “is a part of,” is required.
• Containment (“is inside of”, “is contained in”)
An object may be inside something, but this does not mean it is part of
it. For example, the water contained in a glass is not part of the glass.
• Membership (“is a member of”)
Being part of a group actually refers to being a member of that group.
While “is part of” is transitive, membership is not. For example, while my
arm is part of me, it is not part of the committee I sit on—because the latter
relationship is one of membership.
• Constituents (“made of,” “is a constituent of”)
While a statue may be made of stone, the stone is not part of the statue
with the same meaning as an arm is part of the statue.
• Connections and branches (“is connected to”)
We may want to distinguish between things that are connected to a sys-
tem, say a railway network, and things that are part of the network itself.
So, in an integrated transport network in a city, for example, a bus route will
be connected to the railway network, although it is not part of the network
itself. More subtly, a lamp connected to the electricity system is not part of
the electricity system.
All these alternatives to “part of” offer ways of adding nuanced meaning to
a n ontolog y.
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