SUO: Re: Web-based ontology browsers
----- Original Message -----
From: "Seth Russell" <seth@robustai.net>
To: "Robert E. Kent" <rekent@ontologos.org>
Cc: "Philip Jackson" <phil.jackson@computer.org>; "SUO"
<standard-upper-ontology@ieee.org>
Sent: Monday, September 03, 2001 11:48 AM
Subject: Re: Web-based ontology browsers
<snip>
> Forget about the diagram, do the two mappings you refer to as 'f' and 'g'
> need to be manually entered ??
Assuming 'f' is the instance function of an infomorphism and 'g' is the type
function of same, the answer is yes and no.
When defining an infomorphism from scratch (i.e. at the bottom of a build)
then you do need to populate these functions. As an example, take a look at
the infomorphism named 'punc-type' in the second example on the attached
PDF file.
In general, for an infomorphism named 'F', that is being built from scratch,
the entry statements would look like the following:
(= ((cls.info$instance F) i2) i1)
for instance 'i2' in the target classification and instance 'i1' in the
source classification
(= ((cls.info$type F) t1) t2)
for type 't1' in the source classification and type 't2' in the target
classification.
However, infomorphisms are centrally involved in the specification and
construction of colimits of classifications. Here they are more implicitly
defined. When asserting existence of a sum (coproduct) classification, there
are two sum component infomorphisms automatically produced. And when
creating a quotient (coequalizer or pushout) classification using an
invariant, there is a canoncial quotient infomorphism automatically
produced.
> >In the IFF
> > Foundation Ontology the axioms for infomorphisms are complete (not meant
> > logically, but intuitively).
>
> What do you mean by 'not meant logically, but intuitively' ?
I mean that they precisely and adequately represent the intuitive
mathematical notion.
<snip>
> > > I am having troubles understanding the level of abstraction of your
> > papers.
> >
> > It is fairly high -- after all, it is category theory (see
> > [http://www.mta.ca/~cat-dist/categories.html]).
>
> Category theory doesn't scare me per se (i have always suspected that the
> diagrams I have been drawing for the past 20 years are really expressing
the
> same things that are expressed by category theory diagrams). But I think
> that if IFF is supposed to be a method for growing ontologies, and if we
> want it to become widely used, then the methods need to be accessible to
> those of us who don't want to spend years digesting category theory. I
> think we need IFF translated into natural language understanding. The
> natural language in your paper was quite understandable, and even
> inspirational ... yet when you got to the point of 'how to make it work'
it
> became inaccessible
I think my discussion of role types and visibilty
[http://grouper.ieee.org/groups/suo/email/msg05960.html] may help here.
And also, later versions of the IFF Foundation Ontology, version (2.0)
axiomatizing concept lattices and version (3.0) axiomatizing IF model
theory, should be more concrete (and helpful).
Robert E. Kent
rekent@ontologos.org
Example.pdf