[Crm-sig] superproperty vs subproperty ISSUE?
c.e.s.ore at iln.uio.no
Tue Apr 26 16:11:17 EEST 2011
On 26.04.2011 14:12, Synapse Computing Oy wrote:
Yes and no. Assume you manage to produce an well defined classes that
cannot be further sub divided. You will still have the same problem as
long as one has a super property between superclasses.
A more basal problem is that natural language (as used people) cannot be
formalized into a single formal ontology.
> 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.
> Best regards,
> Synapse Computing Oy, Arabiankatu 2, 00560 Helsinki
> info at synapse-computing.com
> puh/tel/phone +358-41-5499004
> *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?
> Dear all,
> 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
> In English:
> 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
> introduction below).
> A subproperty is a property that is a specialization of another
> (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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