[topicmapmail] Hierarchy PSIs

[tpassin@comcast.net]

Murray  - 
> Tom,
> 
> I certainly believe Bernard is more qualified to answer this
> than I (his mathematical chops are better than mine), but I
> think you may be misinterpreting "partial", which isn't the
> converse of "strict". 

I understand "partial ordering" as meaning that some items may not be ordered by the ordering rules.  Thus, times in UTC can be ordered, and times without UTC can be ordered, but they cannot be ordered together.  I think this notion fits, although I see from your recreation of Sowa's diagram that "Trees" is below "PartialOrdering".  I had in mind trees, but thought that partial ordering would allow more generality without greatly complicating the nature of "virtual" hierarchies.

> In creating an 'ur-hierarchy', I believe
> one must also create definitions for sets, collections,
> classes, and the like, and define membership in terms of
> intentionality or extensionality. Absent this people will
> generally misinterpret the various things available to them,
> e.g., conflating sets and collections.
> 

It depends on whether you want to put together an adhoc tree or need to really specify some strict kind of classification system, I would say.  I would sertainly like to see some standard definitions of various collection classes (or even classes themselves).  BTW, Wordnet 2 has the following for "class" (sense 4)

"class, category, family -- (a collection of things sharing a common attribute; "there are two classes of detergents")"

and for "category" -

"category -- (a general concept that marks divisions or coordinations in a conceptual scheme)"

> But I think we are onto something. Since I believe we've all
> referenced Sowa, one look at Figure 2.14 (p.95 of KR) shows
> a generalization hierarchy, and that PartialOrdering may be
> the place we want to start. I'll try to reproduce a bit of
> that diagram here:

Wow, how long did that take you?

<aside>For those of us who favor ideas of the inherently embodied nature of concepts, notice how the Wordnet definition of category is expressed as a metaphor ("marks divisions")</aside>

Anyway, my main point is that there are good uses for more than one kind of such relationships.

Cheers,

Tom P