Re: SUO: *Date 19 Mar 2002 -- Modus Ponens
Jean Luc,
> As for including "Mereotopology", "Category theory", "Topoi", whatever,
> in a shared ontology this is plainly GROTESQUE, it is the ALGOL-68
syndrom,
> it looks that it would make sense but it is actually useless.
>
> It is just the other way around, even for mathematical theories,
> simpler mechanisms like the one above will have to be used to reconcile
> terminologies from different authors and subtle differences between
> neighbouring theories.
I certainly agree that simpler mechanisms are better, and clearly we do not
want to experience either the ALGOL-68 syndrome or the ADA syndrome. Whether
your programming language analogy is appropriate here I do not know and
will not comment on. However, let me make some hopefully clarifying comments
about the present SUO starter document called the IFF Foundation Ontology
<http://suo.ieee.org/IFF/versions/20020102/IFFFoundationOntology.htm>.
You seem to advocate an FCA approach. However, the IFF already incorporates
a base-line axiomatization for FCA in the IFF Classification Ontology
http://suo.ieee.org/IFF/versions/20020102/IFFClassificationOntology.pdf.
Now the IFF approach also includes a base-line category theory
axiomatization in the IFF Category Theory Ontology
http://suo.ieee.org/IFF/versions/20020102/IFFCategoryTheoryOntology.pdf.
And I agree that including category theory could be grotesque if it did not
have a purpose.
But the IFF Classification Ontology axiomatizes the content of the paper
"Distributed Conceptual Structures"
http://www.kub.nl/faculteiten/fww/medewerkers/swart/conference/rmcs2001.html
where is it shown that the *basic theorem of FCA* can be represented as a
categorical equivalence (actually three categorical equivalences). So the
category theory in IFF already has an indirect purpose -- it is indirect
since the Classification Ontology uses set-theoretically generic notions.
However, the IFF Model Theory Ontology (out next month) is categorically
presented, and it uses only set-theoretically large notions.and axiomatizes
only set-theoretically small notions. This means that the category theory in
the IFF Category Theory Ontology can and will be directly applied to it, in
order to describe the categories, functors and natural transformations
involved in its approach to model theory.
Robert E. Kent
rekent@ontologos.org