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Re: [ontolog-forum] quadruples talk

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Chris Menzel <cmenzel@xxxxxxxx>
Date: Fri, 7 Sep 2007 11:20:36 -0500
Message-id: <20070907162036.GS16682@xxxxxxxx>
On Fri, Sep 07, 2007 at 05:08:03PM +0200, Peter F Brown wrote:
> 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?     (01)

Nothing whatever.    (02)

> And who decides which one to pick?    (03)

No one should be able to, though one might limit tuple length for
purposes of tractable reasoning.  In general, however, for
representational purposes, there should be no upper limit on tuple
length.  As Pat notes, ISO Common Logic permits tuples of any finite
length, even with a single relation.    (04)

> Didn't Keith Devlin first field the idea of "infons", as
> poly-dimensional tuples?     (05)

Well, not really.  "infon" was coined in the late 80s by Jon Barwise
who, initially with John Perry in _Situations and Attitudes_ and
subsequently in collaboration with a lot of other folks, created
situation theory.  Infons themselves are not mere tuples, but structured
pieces of "atomic" information consisting of a relation (in intension,
not a set of n-tuples), some appropriate number of objects filling the
various "roles" of the relation, and a "polarity", indicating that the
objects in the infon do or do not (depending on the polarity) stand in
the relation.  The rather ridiculously productive Prof Devlin worked out
the ideas of early situation theory somewhat informally in his 1991 book
_Logic and Information_, but I believe the theory was in fact developed
more successfully and with much greater rigor by Barwise himself
together with Jerry Seligman in their 1997 book _Information Flow_.    (06)

Applications of IF logics to ontology integration are explored by two
very good European researchers Marco Schorlemmer and Yannis Kalfoglou in
the following papers:    (07)

http://users.ecs.soton.ac.uk/yk1/MCN04-schorlemmer-kalfoglou.pdf    (08)

http://users.ecs.soton.ac.uk/yk1/ifmap-jds03.pdf    (09)

-chris    (010)

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