Re: SUO: Composing Ontologies using morphisms and colimits
I'm a bit behind in my SUO email reading, but I want to comment on
Robert Kent's proposal for relating ontologies via morphisms
and composing them using colimits.
I think this idea has tremendous potential. One problem is that the underlying
formal semantics of category theory is NOT set theory (which is what KIF uses),
furthermore, I think they may well be incompatible.
So, while this idea is a good one, and very worthy of reserching very
thoroughly, I fear there is may be no practical way to use this approach for
representing the main version of the SUO.
My background on this is to have spent seveal months converting the engineering
math ontology in Ontolingua into Slang, the language of Specware. Slang is
based on category theory. Specware is a system based on category theory which
does two main things:
1. supports creation and combination of 'specifications'
(read Ontology, for our purposes) using powerful composition primitives and the
colimit operation.
2. semi-automatic code generation (not of interest with respect to this email)
A major conclusion that I drew was that the mechanisms for composing ontologies
from chunks was very powerful compared to Ontolingua's. For further details,
with specific examples which show the differences between the composition
primitives of Ontolingua and Slang, see a paper I wrote which was published in
FOIS98, Formal Ontology in Information Systems (not online, I'm afraid). A
longer [and earlier] version of the paper is to be found at:
http://ksi.cpsc.ucalgary.ca/KAW/KAW98/KAW98Proc.html.
Mike