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Re: [ontolog-forum] Heterarchy & Hierarchy, oh my my

To: "ZENG, MARCIA" <mzeng@xxxxxxxx>
Cc: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Fri, 2 May 2008 14:59:06 -0400
Message-id: <p06230901c44111205f85@[192.168.99.142]>
At 9:08 PM -0400 5/1/08, ZENG, MARCIA wrote:
>Check: http://sig.biostr.washington.edu/projects/fm/FAQs.html
>
>Foundational Model of Anatomy (FMA) ontology
>Modeling questions...
>4) What does a merged hierarchy mean and why use one?    (01)

Here's a toy example. Suppose you classify people 
as male vs. female and married vs. single. You 
can make this into a two-level hierarchy tree in 
two ways, depending which distinction you make 
'higher' than the other. But this choice is 
arbitrary; and arbitrary decisions like this are 
bad for interoperation, since they tend to be 
made essentially at random, producing 
incommensurate classification systems. Moreover, 
if you make the male/female division nearest the 
root, then there is no place in the tree for the 
class 'married people (regardless of gender)'. A 
merged hierarchy would have these two divisions 
of the root class represented independently, so 
that there would be two routes back from 'married 
men' to 'people', one representing the selection 
of male (not-female) and the other representing 
the selection of married (not-single). 
Inheritance works as usual within each hierarchy 
tree, and they may be independent, although more 
complex schemes can be used.
The chief advantages are already noted, but 
others include increased efficiency of reasoning 
and greater 'naturalness' in connecting 
classifications with associated properties and 
facts. And, contrary to initial expectations, 
multiple-hierarchy schemes are almost as easy to 
implement as single-tree taxonomies.    (02)

Hope this helps. There is a lot more on this 
general topic (including a foundational 
mathematical theory based on lattice theory) on 
John Sowa's excellent website, which I commend to 
your attention.    (03)

Pat    (04)

>
>Hope it is helpful.
>
>Marcia
>________________________________________
>From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx 
>[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] 
>On Behalf Of Pat Hayes
>Sent: Thursday, May 01, 2008 2:46 PM
>To: Charles P. White
>Cc: [ontolog-forum]
>Subject: Re: [ontolog-forum] Heterarchy & Hierarchy, oh my my
>
>At 10:58 AM -0700 5/1/08, Charles P. White wrote:
>Hello all,
>
>This is my first chime into the conversations so I hope my topic is
>appropriate.
>
>At present, I'm working as the lead of NASA/JPL's Spacecraft Problem
>Reporting System (PRS), which is a web based application where an
>engineer or scientist can report a problem with a spacecraft that is
>in-flight, or under development.  When an "anomaly" is created, it is
>then  automatically dispatched to the proper team of folks that can
>triage and solve the problem, sign, and close the issue.
>
>Presently, we are using a hierarchy to define the structure of the
>individual items that make up the spacecraft.  It is a typical
>parent-child-grandchild relationship.  However, I am running into a
>cases where a child can have more then one non-related parents.
>
>Often referred to as 'multiple inheritance'. 
>They are quite common in ontology work.
>
>  This
>aspect is something that hurts my hierarchical mind.
>
>I have recently found the concept of heterarchy in my knowledge
>management quests and find it maybe the answer.  From Wikipedia, "In
>a group of related items, heterarchy is a state wherein any pair of
>items is likely to be related in two or more differing ways. Whereas
>hierarchies sort groups into progressively smaller categories and
>subcategories, heterarchies divide and unite groups variously,
>according to multiple concerns that emerge or recede from view
>according to perspective."
>
>That sounds like a rather general and permissive 
>kind of definition. Do you really need to go 
>that far? Would it be enough to have something 
>like a hierarchy - a tree - but to allow 
>branches to merge downwards, so that a given 
>entry might be on more than one path from the 
>root? A directed acyclic graph (DAG) rather than 
>a tree? Notice this still has the property that 
>going downwards on any given branch gives you 
>progressively smaller categories, and it rules 
>out 'loops' of inheritance.
>
>
>My challenge/question is, how would define and represent the
>heterarchy in a designator system?  We all know how to express
>hierarchy as 1.3.54.A for example, but when an item has more then one
>parent, how can we express that in an equally simplistic way?
>
>You can't, other than by obvious tricks such as 
>having a collection of such designators for each 
>item. But why do you need to? You can maintain 
>the structure in other ways. For example, an RDF 
>triple store can represent an arbitrary DAG 
>structure, and all that is required is that each 
>entry have a unique name of some kind.
>
>Pat
>
>
>
>Thanks for the bandwidth
>Charles P. White (aka Jet Burns)
>"This sentense has three erors."
>
>
>
>
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