[sc34wg3] Re: Mathematical model (was SAM-issue term-scope-def)

[Sam Hunting]

> To: sc34wg3@isotopicmaps.org
> From: Lars Marius Garshol <larsga@garshol.priv.no>
> Date: 03 Jul 2002 19:27:28 +0200
> Subject: [sc34wg3] Mathematical model (was SAM-issue term-scope-def)
> Reply-To: sc34wg3@isotopicmaps.org
> 
> * Nikita Ogievetsky
> |
> | Well ... computing is applied math.
> | XTM is related to computing and some math here is not bad.
> 
> I agree completely. That doesn't mean that SAM/RM have to be
> mathemathical, but there *is* room for a mathematical model.
> 
> A model theory sounds good, but I know we have some graph-heads in the
> room, and I'm not really competent to judge which will better serve
> our needs. Attempts to enlighten me on the issue are welcome, of
> course

I think "the graph" and model theory are, if not orthogonal, not
necessarialy thogonal :-). One advantage of thinking in graph terms is
that you get metrics -- you can say, "so many nodes in this graph", etc --
so design decisions/performance tuning could presumably based on
suchmetrics. A second reason to think in graph terms is that using it
onemight hope to emulate the success of the relational model (which is, as
Lars points out somewhere, is one of the few unqualified successes of the
last twenty years). But I think that while the RM might enable model
theory as the model theorists might understand it, I don't think it is,
itself, a model theory. (Last I looked at RDF model theory, they'd punted
on reification, so I'm not sure of its real-world utility.)

> | I vehemently agree that topic maps have much less to do with logic
> | and inference than RDF, for example.
> 
> Is that because we've tended to see it that way, or is it inherent in
> topic maps? I don't know, to be honest.
> 
> | But there is certainly some set of axioms that we use to make our
> | judgments.  This set of axioms could be called "Processing Model".
> | Interestingly enough it sounds that neither RM, nor SAM pretend to
> | cover it.
> 
> That is true. The PMTM4 proponents have made "this-is-a-graph-and-
> therefore-maths"-like noises in the past, but I'm not sure if they
> would make the same claim of the RM.

For the purpose of developing metrics, or the purpose of having the
functional (and, dare I say it, the marketing) equivalent of the
relational model, yes, the graph "is maths." I don't think that RM or
TMPM4 either claimed to provide "sets of axioms that we could use to make
judgments" (if that is what is meant by "is maths") -- I don't know what
those words mean. 

Sam Hunting
eTopicality, Inc.

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