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Re: [ontolog-forum] Taxonomies and Ontologies and n-ary relaitons

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Patrick Cassidy <pcassidy@xxxxxxxxxxxxxxxx>
Date: Mon, 18 Jul 2005 22:58:31 -0400
Message-id: <42DC6C57.9050200@xxxxxxxxxxxxxxxx>
Chris --
Two issues here, a diversion and the original topic:    (01)

(1) Diversion first: multiple-arity relations
[chris Menzel wrote]
 > . . . For a number of reasons, not least
 > computational tractability, RDF is designed to express only binary
 > relations between individuals.  For remarkably many purposes, this
 > proves to be adequate.  However, often enough, a complete description of
 > a domain requires relations of higher arity, e.g., a description of the
 > spatial relations between objects on a shop floor might require the
 > BETWEEN relation, which is ternary: . . .    (02)

    I think the need for multiple arity relations is generally underrated.  For 
one thing, there is approximately nothing one can say about instances of 
anything in the real world (except maybe class membership) that does not depend 
on the time at which the assertion was made.  That makes most assertions 
inherently at least ternary.  Of course, one can get around that by reifying a 
binary assertion and wrapping it in a holds-at-time binary relation.  I don't 
know if that will be more computationally complex, but it makes assertions 
unnecessarily obscure and moves unnecessarily far from the common linguistic 
expressions, which can be perfectly unambiguous with only modest restrictions 
on 
syntax and cautious permission of some lexical ambiguity -- providing that it 
can be resolved by the local context.
    The big question is whether the perceived computational benefits of 
binary-only relations outweigh the reduced expressiveness and obscurity of the 
contortions needed to say things of realistic import via binary-only.  My 
personal opinion is that there is little benefit to the reduced expressivity in 
most cases, but it can be useful in come cases.   It would be really nice if 
someone would do a properly controlled experiment to evaluate such issues. 
Anyone know of any studies for realistic problems (not just computational 
complexity/tractability -- fine in itself, but not enough)?    (03)

(2) As for taxonomy versus ontology:
    Different people use the terms in different senses, but I have found a 
useful distinction to be that a "formal taxonomy" is one that has only 
hierarchical (subclass/isa/subtype/hyponomy) relations, where each term 
represents a class of entities, and the classes below it are proper subclasses: 
every instance of a subclass is an instance of the parent class.  More 
expressive is a "semantic network" which is a taxonomy with additional semantic 
relations other than "subclass" between classes.  Most expressive and precise 
is 
the ontology, in which (a) the semantic relations are given precise meaning by 
adding axioms in a well-defined logical language to describe the inferences 
that 
can be deduced from use of semantic relations, and (b) precise distinction 
between classes and instances is recognized.  Ontologies come in different 
levels of expressiveness, but at least some form of inference beyond class 
inclusion and undefined semantic relations is required to be an ontology, 
according to these distinctions.
    Thesauri and informal taxonomies have vaguer relations, which are not 
useful 
for inferencing.  An informal taxonomy may not adhere to the "subclass" link as 
the organizing hierarchical link.  An example is a topic taxonomy, where 
narrower topics may be linked under broader topics, but are not necessarily 
subclasses (birds <- ornithologist).  Thesauri can be very heterogeneous in the 
use of links: the "narrower than" link may commonly be either subclass or part 
-- but is sometimes used to suggest other relations, as in topic taxonomies; 
the 
"related to" link can mean almost anything.
    Bottom line -- if you want to do any inferencing, you need a formal 
ontology.    (04)

(3) New issue: ONTACWG reminder
    This has been mentioned before, but I will repeat it here, as it is 
relevant 
to the taxonomy/ontology question.  I am in the process of organizing a 
subcommittee of the Semantic Interoperability Community of Practice to try to 
find ways to get communities to collaborate more closely in developing 
knowledge 
classification systems -- taxonomies, thesauri, ontologies, and graphical 
systems -- and to adopt and extend a "Common Semantic Model (COSMO)" (upper 
ontology/interlingua) to use it as a conceptual defining vocabulary, to specify 
the meanings of the terms in the community knowledge classification systems, by 
combination and extension of the concepts in the COSMO.  This will create 
accurate links between community knowledge classifications -- formal and 
informal.  There can be near-term benefit in improving the functionality of 
community classifications as navigational guides in browsing search, and the 
longer-term benefits will come from developing a common high-level knowledge 
classification that has a sufficiently large user base to gain the benefits of 
interoperability and accurate semantic communication.    (05)

    The working group is called the "Ontology and Taxonomy Coordinating Working 
Group (ONTACWG)" and the home page is at:
      http://colab.cim3.net/cgi-bin/wiki.pl?OntologyTaxonomyCoordinatingWG    (06)

   This is still in the organizational phase.  I hope to be able to hold the 
first meeting by the end of August.  The project is unfunded at this point, so 
initial progress will depend on the voluntary efforts of participants.  Anyone 
who has an interest in relating knowledge classifications to each other is 
requested to register at the site or contact me (pcassidy at mitre.org/ work: 
732-578-6340/ cell: 908-565-4053).    (07)


     Pat    (08)

===================    (09)

Chris Menzel wrote:    (010)

> On Wed, Jul 13, 2005 at 04:24:33PM -0700, Bob Smith wrote:
> 
>>Hi Duane,
>>
>>You said: > it is about the N to N relationships that exist between 
>>those elements??  
>>...
>>Are the N-Ary ideas of Natasha Noy and Alan Rector relevant?
>>
>>http://www.w3.org/TR/swbp-n-aryRelations/
> 
> 
> I don't think they are directly relevant.  That document has to do with
> inherent expressive limitations built into RDF and the weaker versions
> of OWL (OWL-Lite and OWL-DL).  For a number of reasons, not least
> computational tractability, RDF is designed to express only binary
> relations between individuals.  For remarkably many purposes, this
> proves to be adequate.  However, often enough, a complete description of
> a domain requires relations of higher arity, e.g., a description of the
> spatial relations between objects on a shop floor might require the
> BETWEEN relation, which is ternary: x is BETWEEN y and z.  Roughly, the
> document in question discusses ways of simulating in RDF and OWL some of
> the expressiveness gained by having constructs for higher-arity
> relations without actually adding any new syntactic primitives to those
> languages, and hence without altering their computational properties.
> 
> Chris Menzel
> 
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-- 
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Patrick Cassidy    (012)

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Plainfield, NJ 07062-2054    (013)

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