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Re: [ontolog-forum] Taxonomies and Ontologies

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Duane Nickull <dnickull@xxxxxxxxx>
Date: Wed, 13 Jul 2005 16:55:59 -0700
Message-id: <42D5AA0F.10306@xxxxxxxxx>
Bob:    (01)

Sure.  A hierarchal relationship has Node N, Node N -1 and Node N +1.  
If you examine an API for a common tree (such as JDOM - a java API for 
XML), most of the methods exposed are limited to the hierarchal data 
model and traversal of nodes according to some implied first order 
reference model defining the nature of hierarchal models.  Some of the 
methods can see one or all lower nodes ( Element getChild(String 
ElementName), getChildren (List ChildElements) ) and some can see the 
upper nodes (GetParent() etc...).  In a true N to N model, you should be 
able to set and get all associations, regardless of the strict 
hierarchal relationships.  Accordingly, if your model has those N to N 
associations, a hierarchic data model may not be a good choice to try 
and express your model.    (02)

Presume an example hierarchic model where there is a high level element 
A, it has two children B and C, and B has children D and E and C has 
children F and G.   Using only the hierarchic model, you can infer that 
they have the stereotypical hierarchic relationships (Child-parent, 
sibling, isAncestor etc. etc).  What is missing is a more robust N to N 
association where we can also state that in addition to F and G being 
siblings, F is associated with B in named binary association called 
"foo".  In short - any single node of the hierarchy has the ability to 
declare an association to any other node OUTSIDE of the hierarchal 
relationships of the model.    (03)

Accordingly, I have noted that strict hierarchal data models are not 
robust enough to describe all relationships.  I have noted that many 
taxonomies tend to constrain themselves to the hierarchal data model.  
My question is "Is this by design?" or are the designers potentially 
unaware of the constraints imposed on expressing all associations 
possible in a relational model?  This is sort of a relic from the XML 
and Database holy wars/discussion topics on the XML Dev List back in the 
late 1990's.  It seems that ID and IDREF solved a lot of that in XML, 
however many modelers continue to equate taxonomy to hierarchy.     (04)

I think that the N-Ary conversation is relevant however the 
interpretation I got was that is still focused on node to node binary 
associations (I am using Node rather than class here on purpose).  SUMO 
does very well IMO to denote the many forms of association possible:    (05)

a &%SetOrClass if it is an instance of the &%SetOrClass and it is not an 
instance of a proper subclass of &%SetOrClass.")    (06)

   (immediateInstance ?ENTITY ?CLASS)
   (not (exists (?SUBCLASS)
         (subclass ?SUBCLASS ?CLASS)
         (not (equal ?SUBCLASS ?CLASS))
         (instance ?ENTITY ?SUBCLASS)))))    (07)

(instance inverse BinaryPredicate)
(instance inverse IrreflexiveRelation)
(instance inverse IntransitiveRelation)
(instance inverse SymmetricRelation)
(domain inverse 1 BinaryRelation)
(domain inverse 2 BinaryRelation)
....<SNIP> - go look up in SUMO.    (08)

So the questions I now pose are:    (09)

1. Are all taxonomies hierachal data models?  It seems to be common, yet 
I am not sure if "hierarchal" is a core property of any taxonomy.
2. Are all ontologies able to be expressed solely in hierarchies?  I 
would think the answer is no but it seems that many people have a 
tendency to favour this.  SUO KIF does very well IMO in being able to 
move beyond hierarchic relationships and expressions.    (010)

On a related note, I have also noted that I could not find any 
conventions for a class of models referred to as Concept Maps or Mind 
Maps.  I am in the process of penning a paper on Concept Map conventions 
which at first seemed like it would be a five minute job but now seems 
to be much more involved.  If anyone is interested in that work, I can 
provide a link.    (011)

Duane    (012)

Bob Smith wrote:    (013)

>Hi Duane,
>You said: > it is about the N to N relationships that exist between 
>those elements??  
>Could expand on these "N to N" ideas a little?
>Are the N-Ary ideas of Natasha Noy and Alan Rector relevant?
>(Background: Rex Brooks, Peter Yim, myself, and several others are
>considering the "Health Informatics Standards Landscape" and the complex
>relationships may be better described initially with graphs rather than a
>-----Original Message-----
>From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
>[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Duane Nickull
>Sent: Wednesday, July 13, 2005 3:31 PM
>To: [ontolog-forum]
>Subject: Re: [ontolog-forum] Taxonomies and Ontologies
>Brian (Bo) Newman wrote:
>>While perhaps not semantically complete,  I have found it quite useful 
>>(in presentations to those outside of the ontological communities) by 
>>anchoring such discussions with; "A class hierarchy may also be called 
>>a taxonomy" [1] -- "taxonomies are methods for describing 
>>classification relationships" [2]; explaining that ontologies (formal 
>>or otherwise) provide additional semantic elements that allow them to 
>>covey more meaning that just what is provided by a taxonomy. 
>DN - would it be fair to extend this to also state that the ontology is 
>also about the relationships between the elements of a taxonomy in 
>addition to the hierarchal nature of their associations?  An ontology is 
>about more that just the elements of a taxonomy and their individual 
>semantics - it is about the N to N relationships that exist between 
>those elements??  Could one infer that Taxonomies are always scoped to 
>only represent hierarchal relationships between elements?  I see a lot 
>of people who seem to infer this but have never seen it written in black 
>and white.
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