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Re: [ontolog-forum] Category theory and ontologies

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Sat, 12 Jul 2014 08:21:50 -0400
Message-id: <53C1285E.7090104@xxxxxxxxxxx>
Leo,    (01)

I had not forgotten IFF, Robert Kent, or OntoIOP.    (02)

> Probably folks tend to forget Robert Kent's original
> contributions at the IEEE-SUO list/standards effort on
> category theory with respect to ontologies.    (03)

I was one of the early advocates for making IFF an official SUO
project.  It's too bad that he hadn't been able to get more support
for completing and extending that work.    (04)

> Till Mossakowski and others are using Goguen’s theory of
> institutions for ontology mapping, including in the current
> OntoIOp effort: http://about.ontohub.org/ontoiop.html.    (05)

And I believe that OntoIOP is developing some important methods
for mapping ontologies.    (06)

But the word 'category' when used to discuss the categories of
an ontology has a different sense from the word 'category' when
used as the name of category theory, the mathematical system.
The terms 'IFF' and 'institution' are much less likely to cause
confusion.    (07)

While we're speaking of Joseph Goguen and formal systems, note
his article, "Tossing algebraic flowers down the great divide":
http://cseweb.ucsd.edu/~goguen/pps/tcs97.pdf    (08)

 From p. 13 of that article:
> It is (or should be) a scandal that in the middle of a period
> called the "information age" and characterized by an astonishing
> expansion of information technology, there is no adequate theory
> of information nor even an adequate definition of information.    (09)

Goguen raises some very serious questions about how, when, and whether
formal methods can or should be used.  It's interesting to note that
he wrote his PhD dissertation on fuzzy set theory with Lotfi Zadeh
as his thesis adviser.    (010)

John    (011)

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