[Crm-sig] superproperty vs subproperty ISSUE?

Christian-Emil Ore 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,
> Mika
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> 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
>     Glossary:
>     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
>     etc.
>     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.
>     *************
>     CRM:
>     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).
>     regards,
>     Christian-Emil
>     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
>     superproperty,
>     2. the intension of the subproperty extends the intension of the
>     superproperty, i.e. its traits are more restrictive than that of its
>     superproperty,
>     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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