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Re: [ontolog-forum] N-RELATIONs: Formal Ontology, Semantic Web and Smart

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>, glenn mcdonald <glenn@xxxxxxxxx>
From: Ali SH <asaegyn+out@xxxxxxxxx>
Date: Mon, 7 Nov 2011 12:28:13 -0500
Message-id: <CADr70E2gpUJyqjQoMpPXo+2RkoMZC5nOcAHheKYXpretwqB7vw@xxxxxxxxxxxxxx>

I followed up with Glenn who had made that initial comment (I'd thought perhaps he was using hypergraphs to model them).

He responded thusly:

I mean that in a graph you can have a node representing the relation itself. This node can have any number of outbound arcs to the nodes that are part of the relation. So to model a marriage as a n-ary relation with a time-span and two spouses, we have

- Time-span -> 1989-2004
- Spouse -> Mabel Augury
- Spouse -> Adam Dowswer
This approach is no different, ultimately, from relational modeling in the original sense of the term. It's only breaking things into triples that makes it seem hard.

Which basically seems like reifying the relations - the relations are now also nodes, not just the edges.


On Mon, Nov 7, 2011 at 12:04 PM, AzamatAbdoullaev <abdoul@xxxxxxxxxxxxxx> wrote:
Friday, November 04, 2011 5:47 PM, David Price wrote:
"WRT RDF doesn't it simply boil down to being based on graphs which,
> quoting from Wikipedia, are "mathematical structures used to model
> pairwise relations between objects from a certain collection". So, I'm
> confused by comments like "N-ary relations work great in a graph model."
> which seems completely at odds with the fact that graph relations are
> pairwise."

Any graph, as an ordered pair of vertices/nodes/points and
edges/links/lines, is a type of binary, two-place or dyadic relation. But an
N-relation R is a relation over the sets X1, ., Xn , which is a (n +
1)-tuple R = (X1, ., Xn, G(R)), where G(R) is a subset of the Cartesian
product X1 × . × Xn where G(R) is the graph of R.
There is also another widespread issue with relations, they are mostly given
an extensional interpretation, assuming that the extension of a relation is
the relation itself.



(•`'·.¸(`'·.¸(•)¸.·'´)¸.·'´•) .,.,

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