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Re: [ontolog-forum] Types of Formal (logical) Definitions inontology

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Wed, 09 Jul 2014 13:01:51 -0400
Message-id: <53BD757F.5070503@xxxxxxxxxxx>
Frank, Henson, and Ed,    (01)

> Given the discussions on Category Theory, I was curious if the
> community views Predicates as a form of categorization/classification.    (02)

Two points:    (03)

  1. Category theory is a mathematical system that might be used for
     ontology.  But if you have to ask what it is, don't use it.
     Brief summary:  http://en.wikipedia.org/wiki/Category_theory    (04)

  2. Every class, type, or category in any ontology can be associated
     with a predicate that is true of everything in the class, type,
     or category and false of everything not in it.    (05)

> I believe the problem is that OWL axiom sets always have a tree
> model whether you want it or not. OWL axiom sets may have other
> models which are not trees.    (06)

> Not quite 'trees' -- classification lattices, with 'property links'
> that produce more or less general semantic networks, including cycles.    (07)

I agree with Henson.  The OWL *classes* are organized in lattices.
But the *models* (in Tarski's sense) are limited to trees.    (08)

For example, a benzene ring has a cycle.  OWL cannot state the
critical properties that require a model of benzene to have a cycle.    (09)

Just look at any bridge truss, and you'll find interconnected
triangles that create huge numbers of cycles.  It's impossible
to find any complex artifact or biological system without cycles.
OWL cannot specify, analyze, or reason about those cycles.    (010)

> Where they have problems is in constructing OWL axiom sets for
> a molecule such as H2O which constrains the models to only consist
> of molecules with exactly three atoms. There are a lot of papers
> by Horrocks and Motik and students on this topic.    (011)

I know Horrocks and Motik.   They're intelligent, but they're
hopelessly *arrogant* to claim that they are qualified to tell
experts in every branch of science, engineering, and business
what models they're allowed to use, represent, and reason with.    (012)

> This has led them to try graph extensions of DL and logic
> programming extensions.    (013)

Yes.  And every one of those extensions adds more and more complexities
to an overly complex system.  By comparison, the LP systems are easier
to learn and use and far more efficient for equivalent applications.    (014)

Programmers and computer scientists have had far better methods
for controlling complexity and avoiding issues of undecidability.
They use various terms:  structured programming, structured
analysis, design patterns, and knowledge compilers.    (015)

When I wrote my article "Fads and Fallacies in Logic", the primary
fad I had in mind was OWL.  And the primary fallacy was decidability
as the bogeyman:  http://www.jfsowa.com/pubs/fflogic.pdf    (016)

By the way, Jim Hendler was the editor of the journal in which it
was published.  And he liked that article very much.    (017)

John    (018)

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