[Crm-sig] superproperty vs subproperty ISSUE?
Synapse Computing Oy
info at synapse-computing.com
Tue Apr 26 15:12:36 EEST 2011
The problem is of course trivial in the sense that there is a hidden distinction, the property of sex, which subdivides persons into men and women and groups into males and females.
The way to acheive filtering is thus to make the implicit distinction explicit by introducing a new distinctive feature into the class definition (intension) of person resulting in a further subdivision of (the extension of) person into male and female.
A situation like this might arise when distinctions are made based on a intuitive understanding of language instead of a formal specification of the intension of concepts/classes. In formal systems these kind of ambiguities pop up. One interesting tool to detect these kind of traps is Alloy http://alloy.mit.edu.
Thus, the flaw is not with the inheritance mechanism but with a too slack definition of classes.
Synapse Computing Oy, Arabiankatu 2, 00560 Helsinki
info at synapse-computing.com
From: Christian-Emil Ore [mailto:c.e.s.ore at iln.uio.no]
To: crm-sig [mailto:crm-sig at ics.forth.gr]
Sent: Tue, 26 Apr 2011 14:37:06 +0300
Subject: [Crm-sig] superproperty vs subproperty ISSUE?
As a preparation of a lecture I gave some weeks ago, I closely studied
the Danish WordNet and found some peculiarities due to to freely
inheritance of properties
mand = man
mandfolk = men (collective)
person = person
gruppe = group
inngår i = is_a_member_of
mand ISA person
mandfolk ISA group
person inngår i gruppe
man ISA person
men ISA group
person is_a_member_of group
With unrestricted inheritance of properties of a superclass we get
man is_a_member_of men (OK)
person is_a_member_of men (not OK)
The latter implies that any person can be a member of men, even my
little daughter. This is clearly ontological nonsense.
I discussed this with the editor of the Danish Wordnet, Bolette
Pedersen, and the inheritance system had been discussed in their group,
but apparently no solution had been found.
In a logical/mathamatical setting it is evident that if
f: A -> B and
B' a subset of B, then one cannot in general assume that
f: A -> B' is well defined for all a in A.
In CRM there are no restrictions on inheritance of properties. So the
subclass hierarchy has to be/been designed with care so that the model
is not turned into expressed nonsense.
My questions are: Is this restriction a problem? Should a mechanism for
filtering/restricting property inheritance be introduced? (The current
subproperty is not imposing any restriction see the quite from the
A subproperty is a property that is a specialization of another property
(its superproperty). Specialization or IsA relationship means that:
1. all instances of the subproperty are also instances of its
2. the intension of the subproperty extends the intension of the
superproperty, i.e. its traits are more restrictive than that of its
3. the domain of the subproperty is the same as the domain of its
superproperty or a subclass of that domain,
4. the range of the subproperty is the same as the range of its
superproperty or a subclass of that range,
5. the subproperty inherits the definition of all of the properties
declared for its superproperty without exceptions (strict inheritance),
in addition to having none, one or more properties of its own.
A subproperty can have more than one immediate superproperty and
consequently inherits the properties of all of its superproperties
(multiple inheritance). The IsA relationship or specialization between
two or more properties gives rise to the structure we call a property
hierarchy. The IsA relationship is transitive and may not be cyclic.
Some object-oriented languages, such as C++, have no equivalent to the
specialization of properties.
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