SUO: Re: [Fwd: Re: Ontology mapping]
Jim, Leo and others,
> 2) But I think the issues I raised are practical ones that even the IFF
> will be called upon to deal with at some point. I am not saying that the
> IFF itself should address how one goes about identifying, say, theories
> or models from ontologies, but at some point past the hand-tailored
examples
> that we will use for the IFF (which will necessarily, I think, make some
> assumptions about commonality of language features), one will need to face
> the issue that there are ontologies like Cyc and SUMO that we would want
> to be able to put in the IFF framework.
This may not help with your more practical problems, but may be of some
interest to you and other SUO-folk. The IFF Model Theory Ontology (IFF-MT)
focuses on the means of expression, not the content. The IFF-MT contains
much terminology, some of which functions purely in a supporting role and
some of which will be in direct use by applications. The latter might be
called the _IFF-MT interface_. Now three central terms in the interface of
the IFF-MT are *model*, *language* and *interpretation*.
In application, a central goal would be to show how any 1st-order expressed
content can be mapped into a *model* of the IFF. This involves identifying
and mapping features of various ontological languages (CGIF, CycL, CL) into
the IFF-MT terminology. The IFF-MT document shows how to do this for any
*knowledge base* discussed in the Conceptual Graphs Standard
http://users.bestweb.net/~sowa/cg/cgstandw.htm .
Now each model has an associated 1st-order (type) *language* out of which
its expressions (formula) are built -- this of course consists of the names
for the relations (with associated valences, arities and signatures),
functions and constants that it uses. Once content is mapped into the models
of the IFF-MT, one standard method of comparison between IFF models is the
definition of a 1st-order *interpretation* of the IFF (see page 74 of
Barwise and Seligman "Information Flow: The Logic of Distributed Systems").
Each 1st-order interpretation is a morphism between two 1st-order languages.
Interpretations map the relations of one 1st-order language to the
expressions (formula) of another 1st-order language.
A central fact to recognize is that each IFF interpretation maps
functorially to a *truth infomorphism* -- that is, a morphism between the
*truth concept lattices* of the two 1st-order languages. (see page 74-75 of
Barwise and Seligman for an rudimentary discussion). Truth concept lattices
and truth infomorphisms are expressible using the terminology in the IFF
Upper Classification Ontology (IFF-UC)
<http://suo.ieee.org/IFF/versions/20020102/IFFClassificationOntology.pdf>.
Diagrams of truth concept lattices and truth infomorphisms, which are built
up in this way, can be internalized into a single concept lattice via the
colimit operation in the IFF-UC.
So in the IFF the specification of 1st-order interpretations is a key
approach for building lattices of theories.
Robert E. Kent
rekent@ontologos.org