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   Re: [xml-dev] Ontologies and fuzzy set

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Didier PH Martin wrote:

> ...I had a hard time to "explicitly" model set ownership fuzziness in
> OWL or OIL. To say the least I failed to be able to model the real world
> with OWL or OIL. 

This is not surprising, because OWL is all about extentions - the set of 
members in the set associated with an OWL class.  You are either in the 
extention of the class or not.  No wonder you cannot get fuzzy 
membership in an OWL class.

It would be awkward in RDF, as well, since a membership qualified by a 
number is inherently a three-part relationship, which you do not 
directly have in RDF.  You could create a node of type "membership" -

    member dog
    degree .9

Then you could create a "fuzzy set" resource - maybe "pet" in this 
example - that is related to the membership node.

> Issue: 
> ------
> Can I "explicitly" model set ownership when this very relationship is fuzzy
> and not Boolean (as it is most of the time in the real world).

John Sowa has written that it takes three steps to moel the world, not two

1) A lattice of theorems (i.e., a purely mathematical structure)
2) A model, that stands between the world and the lattice.
3) The world itself.

In this scheme, the model maps to the lattice of theories in a binary, 
true/false manner, while the model maps to the world in a fuzzy way. 
Thus, OWL classes would map between theorems and the model.  There would 
be no need to try to force the model to map to the world in a crisp, 
true/false way.

I don't know if this has been helpful, but at least it is interesting.


Tom P


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