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Re: [ontolog-forum] Next steps in using ontologies as standards

To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Matthew West <dr.matthew.west@xxxxxxxxx>
Date: Tue, 27 Jan 2009 08:48:48 -0000
Message-id: <497eca89.2f89260a.487f.08ab@xxxxxxxxxxxxx>
Dear Mitch,    (01)

We seem to be more or less on the same page.    (02)

> >
> > > I was unaware that Category Theory was distinct from logic.
> 
> It's all math. Category theory is usually considered coming out of the
> subdomain of algebra (though its primary examples are in topology;
> logic (-mathematical- logic that is) is usually considered a quite
> separate subdomain of mathematics. That said, you can make meaningful
> connections between any two subdomains (e.g. Categorical logic).
> 
> > Category Theory is an alternative foundation.
> 
> Yes, but that's at a different idea of foundation. Logic (and set
> theory is considered a foundation of mathematics  with respect to
> truth. Category theory provides a foundation
> 
> > You can for example describe logic in terms of category theory.
> 
> And you can describe category theory in terms of logic.    (03)

[MW] Indeed, that is what  I meant by being an alternative foundation.
> 
> I think category theory is a red herring here (as well are probably
> most of my comments). Category theory is a fascinating unifying theory
> of mathematics, and is also quite useful in its applications to
> programming language semantics, I would think that any benefit that
> you could get out of it would be way beyond the learning curve. And
> that benefit could be gotten with, well, simplifying to semantic
> networks, though I'm sure there are some nice tricks that category
> theory provides that logic (logical theories?) can use.    (04)

[MW] Actually I think Category Theory may provide some useful ways to do
inferencing in a more structural way, but that is really just a hunch (or
conjecture if you want to be a bit more formal).    (05)

Regards    (06)

Matthew West                            
Information  Junction
Tel: +44 560 302 3685
Mobile: +44 750 3385279
matthew.west@xxxxxxxxxxxxxxxxxxxxxxxxx
http://www.matthew-west.org.uk/    (07)

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> 
> Which is all to say that mathematical formalisms are pretty useful
> whether we are using something called category theory or one of the
> many varieties of logic.
> 
> --
> Mitch Harris
> 
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