[topicmapmail] Hierarchy PSIs

[Murray Altheim]

tpassin@comcast.net wrote:
> 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.

Not really, but Bernard answered this in his reply better than I
could.

I think what a lot of situations call for is simply "relation
direction", which is essentially just a recognition of which is
subject and which is object in a sentence. When you have a set
of sentences (which is a term used to describe a theory or
ontology, depending on the context), being able to order across
a group of them is called "partially ordered" when antisymmetry,
transitivity or reflexivity are present. But like I said, Bernard
said this better.

The PSIs I developed for Ceryle were initially just designed for
this purpose (to show direction in a visualized graph), but I've
been trying to formalize this because I *do* want to inference
on some of the relations.

>>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).  

Well, one of the intentions I have is to publish all of the
PSI sets I used in Ceryle's authoring ontology, and amongst
them would certainly be such things. Sorta a mini Cyc.

> 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)"

The "danger" here is that there are two things going on: one,
an attempt to come up with relatively formalized definitions
for relation and role types in order to establish an ability
to inference (even for minor inferencing such as traversal),
and in WordNet, the much more informal use of natural language.

>>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?

Bernard noted I made a mistake, but about ten minutes. I
have been honing my ASCII chops since hanging around with
Jon Awbrey. :-)

> <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.

Absolutely.

Murray

......................................................................
Murray Altheim                    http://kmi.open.ac.uk/people/murray/
Knowledge Media Institute
The Open University, Milton Keynes, Bucks, MK7 6AA, UK               .

    "The US Government has expanded its recall of beef after the
     discovery of its first case of "mad cow" disease. Officials
     had said the meat from the infected cow, slaughtered on
     9 December in Washington State, went to Oregon, California,
     Nevada and Washington. They have now determined that meat
     from the same facility, killed on the same day, went to
     Alaska, Hawaii, Montana, Idaho and the territory of Guam."
     http://news.bbc.co.uk/1/hi/world/americas/3352911.stm

   One cow distributed across nine states and territories. Maybe
   if we were buying meat raised and slaughtered locally, and not
   feeding meat to herbivores (to increase profit, not quality)
   this might not have happened.