Categories, Universals, Particulars

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Categories, Universals, Particulars

Patrick Browne
Below are some assumptions which are followed by two questions.

1. Categories are high level generic concepts e.g. Region

2. Universals are classes of actual things and particulars e.g. Country

3 Particulars are individual occurrences of universals e.g. Ireland

4. Categories are organized using subsumption hierarchies
(mathematically a sub-set relation).

5. Universals are organized using subsumption hierarchies
(mathematically a sub-set relation).

6. Individuals are elements of sets (mathematically element-of or set-
membership relation)


Question 1: Are these assumptions correct?

Question 2: Is the relationship between Categories and Universals also
subsumption, with the caveat the categories are higher up the hierarchy
than universals?


If this is not an appropriate forum for these questions then perhaps
someone could suggest an alternative mailing list.

Thanks,
Pat

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Re: Categories, Universals, Particulars

Thomas Russ
For modeling in OWL you of course get classes, properties and individuals.

Your questions don't deal with properties, but do introduce two varieties of classes, which is a distinction that OWL doesn't draw.

On Jul 24, 2011, at 5:37 AM, Patrick Browne wrote:

> Below are some assumptions which are followed by two questions.
>
> 1. Categories are high level generic concepts e.g. Region
>
> 2. Universals are classes of actual things and particulars e.g. Country

In OWL, you would model both of these as classes.  One does have to wonder whether you can even be certain of universals, at least in the sense of there not being any subclasses of them.  So for your example of Country, what about if you later decide to create EuropeanCountry.  Does that then make Country no longer be a universal?

The two useful distinctions that OWL does make are fully and partially defined classes.  Fully defined classes have an equivalent definition that provides necessary and sufficient information.  This is used to automatically recognize individuals.  The definitions also serve to allow for automatic classification of classes so that the hierarchy is automatically maintained.

An example of such a defined class could be
   EuropeanCountry == Country and (some inRegion Europe)

> 3 Particulars are individual occurrences of universals e.g. Ireland

These would be individuals.

>
> 4. Categories are organized using subsumption hierarchies
> (mathematically a sub-set relation).
>
> 5. Universals are organized using subsumption hierarchies
> (mathematically a sub-set relation).

Yes, OWL would use the subclassOf property to relate them

> 6. Individuals are elements of sets (mathematically element-of or set-
> membership relation)

This is done using the rdf:type property on the individual.

> Question 1: Are these assumptions correct?
>
> Question 2: Is the relationship between Categories and Universals also
> subsumption, with the caveat the categories are higher up the hierarchy
> than universals?

Well, it pretty much has to be.

But you also need to make sure that you really only use subsumption for the sub-set relationship. In particular, since you use geographic examples, you will want to use a different property to model geographic containment.  That is a part-of type of relation and not subset-of.

So, for example, Continents could be part-of a hemisphere and countries could be part of a continent but they would not be subsets of hemisphere or continent.  The test to consider is whether it is true that an individual of a sub-set is necessarily an individual of the super-set.  So, Ireland could be part-of Europe (a continent), but Ireland would not BE a continent.  That tells you that Country cannot be a subset (subclass) of continent.

> If this is not an appropriate forum for these questions then perhaps
> someone could suggest an alternative mailing list.

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