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Re: category theory

From: Renato Golin <renato@ebi.ac.uk>
Date: Tue, 10 Jul 2007 00:15:12 +0100 (BST)
Message-ID: <47790.>
To: "Ioachim Drugus" <sw@semanticsoft.net>
Cc: "Ivan Herman" <ivan@w3.org>, semantic-web@w3.org

Hi Ioachim,

> Renato
> focus on category theory was due to the emphasis which he puts on
> *context* as I noticed in other threads).  Now, due to its intensional
> approach, OWL describes an open world model, which means that the
> "whole", described by a statement of category  theory, *changes*.
> Because the statements of category theory expressed in OWL would refer
> to the changing world, they might stop to be true on Semantic Web - this
> is one reason why they don't usually take statements of category theory
> into OWL. But when we assign in the *axioms* of DL certain
> "intentionality" to a term which refers to its behavior with respect to
> the whole universe of discourse (as when we state something in
> negative), then it is best to look for the formulations (definitions and
> statements) of category theory and write them in OWL. Therefore, I
> regard category theory as important for the development of semantics of
> Full OWL.

As you said, context is temporal: The whole change at the same speed as
their representations (which is the semantic web). Adding extension
parameters won't invalidate that change as new parameters will be added.

Conflicts will always happen for we can't control all ontologies. One may
think that cousin is not bijective, and it may happen in languages that
cousin have male/female variations (stupid example but you got the

I still have to verify Ivan's terms in my application to see how well (or
bad) it'd fit, though.

> 3. The two main philosophic disciplines, on which Semantic Web is based,
> are Ontology and Epistemology. But how come that something which just
> *exists* and is matter of Ontology, can convey *knowledge* which is
> matter of Epistemology!? I believe, it is Phenomenology, which serves as
> a link between the other two pillars of Semantic Web and it should serve
> as a third pillar. In another message (on clarification what is an
> "information resource") I exposed my view which I named MyPhenomenology,
> where I reduced cognition to *representation* and knowledge to
> *presentation* and stated that category theory is formalization of this
> view.

If you see knowledge as a list of things, an ontology is all you need. But
knowledge is not enough for clever programs, we do have knowledge already
in the old web but we don't know what to do with that.

The importance of the semantic web is to give meaning to all that
(therefore it's name) and category theory is the way I'd give meaning to
the core axioms.

> I also have a 4th aspect of Category Theory strongly correlated with
> Semantic Web, but I would be ready to explose it later.

Let's wait for the next thread... ;)

Btw, I was going to answer your other email about context but it was far
too long... in a nutshell, I agree with most of it... ;)

Received on Monday, 9 July 2007 23:15:33 UTC

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