Patrick Cassidy wrote: (01)
> Chris --
> Two issues here, a diversion and the original topic:
>
> (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: . . .
>
> 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)? (02)
There are important theoretical advantages to binary-only relations.
Practically, I believe it is a matter of GUI tooling to provide support
for organizing n-ary relations in terms of binary ones. (03)
Robert Colomb's paper: Category-Theoretic Fibration as an Abstraction
Mechanism in Information Systems
http://www.itee.uq.edu.au/~colomb/Abstracts.html (04)
Michael Johnson's paper: Entity-relationship-attribute designs and sketches
http://www.tac.mta.ca/tac/volumes/10/3/10-03abs.html (05)
-- Nicolas. (06)
>
>
> Pat
>
> ===================
>
> Chris Menzel wrote:
>
>> 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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> (07)
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