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Re: [ontolog-forum] quadruples talk

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Ed Barkmeyer <edbark@xxxxxxxx>
Date: Fri, 07 Sep 2007 14:29:56 -0400
Message-id: <46E198A4.3020702@xxxxxxxx>
Peter F Brown wrote:    (01)

> Surely everyone has their own use case for another dimension being added.
> Triples are only an "arbitrary" choice of dimensions to the
> extent that they elegantly provide a two-dimension graph of two
> nodes and a single arc: anything above that surely opens the
> case for K-arity rather than "just" quadruples.
> What is special about four dimensions?    (02)

I agree with Peter on this.    (03)

My modeling experience with languages like ORM/NIAM tells me that 
ternary relations are not uncommon, quaternary relations are rare 
and quintenary (quinary?) relations are very rare, but they do 
occur in "business situations" and therefore may occur in ontologies.    (04)

The most common ternary relationship I see is:
  Resource plays Role in Activity
and proper representation of that really needs a quad, rather 
than a reification called "Involvement".    (05)

But in manufacturing capacity planning one regularly sees:
  Process on Material using Machine requires Time
(and ... costs Money and ... requires Capability, etc.)
And these would properly require a 5-tuple.
Of course, this is usually captured by reifying "Process on 
Material using Machine", as long as one is careful not to mistake 
it for the ternary relation: Process on Material uses Machine, 
which represents an implementation decision.    (06)

Further, the List concept is intrinsically variadic, although it 
can be captured as a reification with binary "member" relations 
(noting that this capture makes the relationship AMONG list 
members a "derived" property).    (07)

Finally, I would observe that the most common use of quadruples I 
have seen is to capture some "time" or "version" qualifier on 
binary facts.  (I personally regard this as blind imposition of a 
dimension in lieu of capturing the meaningful relationships to 
time or version.  But one only has the luxury of capturing the 
meaningful relationships if one is designing the ontology/schema 
ab initio.  Just adding a "version" dimension is all that can be 
done without domain knowledge to an existing schema that models 
an instantaneous world.)    (08)

-Ed    (09)

Edward J. Barkmeyer                        Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263                Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263                FAX: +1 301-975-4694    (010)

"The opinions expressed above do not reflect consensus of NIST,
  and have not been reviewed by any Government authority."    (011)

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