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Re: [ontolog-forum] Categorical Views of a Universe

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Thu, 27 Jan 2011 08:11:14 -0500
Message-id: <4D416EF2.4080403@xxxxxxxxxxx>
Doug and Rich,    (01)

> A network of interconnected ontologies on different subject matter or
> ways of looking at the universe (e.g., 3D vs. 4D) is what John Sowa and
> i, among others have been promoting.    (02)

>> Would those ontologies change with time, or just die out as individuals
>> and be replaced by their some chain of descendants, like us    (03)

An ontology is a theory.  Each revision of a theory is a new theory.
Whether you throw the old one away depends on how much storage is
available.  But given today's systems, I would suggest that you keep
each theory ever developed in a hierarchy:    (04)

  1. Adding an axiom to a theory creates a more specialized theory.    (05)

  2. Deleting an axiom creates a more generalized theory.    (06)

  3. Modifying an axiom creates a sibling of a theory that is
     immediately below the same parent as the old theory.    (07)

How you name the theories is independent of the hierarchy, but the
metadata or a name with a version number would be important.    (08)

> we should consider multiple independent ontologies, perhaps
> even weakly and strongly interconnected ones.    (09)

Yes.  If you keep every modification of every ontology, you'll
get a strongly interconnected hierarchy.  But you don't have to
store them all in the same place, and you can highlight some
or deprecate others.    (010)

So you could have links with greater (call it what you like)
strength, salience, importance, etc.  All the paths could be
accessible, but the metadata could add further information,
including recommendations, warnings, prohibitions, etc.    (011)

> Knowledge bases built on the ontologies would change rapidly.  The
> ontologies, themselves, would change at a slower rate.  So long as
> the changes were additions (new types of accounts, genes, products)
> they could remain the "same" ontology -- however, versioning might
> be useful.    (012)

A KB that includes an ontology plus a DB of facts is effectively
a more specialized theory.  That is true of either a 4D or a 3+1 D
approach.  But since the same ontology might be used with a wide
variety of different DBs, it would be useful to keep them distinct
in practice.    (013)

For more detail about the hierarchy of theories, see Sections 5 to 7
(pp. 15 to 25) of the following paper:    (014)

    http://www.jfsowa.com/pubs/rolelog.pdf    (015)

The first 14 pages cover a lot of philosophical and historical
issues.  Skip directly to p. 15 for the hierarchy of theories,
the operations on it, and its use in a versioning system.    (016)

John    (017)

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