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Re: [ontolog-forum] Foundation ontology, CYC, and Mapping

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Thu, 04 Mar 2010 09:56:44 -0500
Message-id: <4B8FCA2C.8000307@xxxxxxxxxxx>
Dear Matthew, Pat, Ali, and Mike,    (01)

MW> ... there is no reasonable chance that we can create an ontology
 > that is right first time, or that at any time after does not have
 > some mistake or improvement that can be made. The best we can hope
 > for is that as it is used and reused, more of the bugs are discovered.    (02)

Yes.  IBM's euphemism for any product that will never change is
'functionally stabilized' -- i.e., it is obsolete and no new version
will ever be produced.    (03)

MW> Fortunately, the relatively straightforward technique of version
 > management comes to our aid. This may be something that needs to
 > be added to a lattice of theories repository that holds the versioning
 > meta-data between different theories that represent the different
 > stages of development.    (04)

The lattice of theories provides an excellent basis for versioning.
The theories in the lattice never change.  But each change to a
theory creates a new theory that is a generalization, specialization,
or sibling of the previous theory.  The metadata that shows how the
theories are related would also include its provenance -- time and
date of creation, by whom, by which tools, and from which starting
theories.  Those starting theories would always be stored somewhere
in the hierarchy.  They may be older versions or some collection
of versions and modules that were combined and modified.    (05)

MW> The downside is that change in the core of the FO may have an
 > impact on the mappings to the FO, which has a cost. The real danger
 > is that the cost of changing those mappings leads to the improvements
 > being rejected.    (06)

I consider the term Foundation Ontology or FO to be an honorary marker,
such as a gold medal in the metadata.  From the point of view of the
lattice, the FO is just one more theory, which is related to the others
by the same basic operators.   A change to the FO consists of taking
away its medal and bestowing it upon a different theory in the lattice.    (07)

MW> I don't see a better strategy though.    (08)

Nor do I.  And so far, the only alternative has been the *hope* that
the FO might be so good that it would never lose its gold medal.    (09)

PC> But mapping every ontology to the FO seems to me to take a lot less
 > effort than generating multiple mappings between the ontologies of
 > that set.    (010)

Creating the mappings is automatic.  It does not require any extra
effort.  The basic operators used to *create* a theory are the same
ones that determine how the theory is related to other theories:
either combining other theories or adding, deleting, or modifying
individual axioms.  The sequence of steps in its creation determines
how a theory is related to its starting theories.    (011)

And note that we distinguish the implemented *hierarchy* as a subset
of the purely theoretical and infinite *lattice*.  There is no
requirement for the hierarchy to specify all possible relationships.
But whenever anybody discovers a relationship, there is always a
place to record it.    (012)

PC> I emphasize that the goals of mapping between domain ontologies
 > and using the FO are not incompatible, I just believe that there
 > are things you can do with an FO that are not possible or not
 > practical by trying to map among multiple ontologies without
 > generating an FO.    (013)

I have no quarrel with treating the FO as a recommended or "gold medal"
theory.  But the point I keep emphasizing is that all the possible
operations with the FO are exactly the same as the operations that
can be performed with any other theory in the hierarchy.    (014)

The beauty of this approach is that every business or industry can
have its own specialized FO (SFO), which is a specialization of the
general FO that has additional axioms and definitions used for that
industry.    (015)

In fact, it's quite possible or even likely, that the SFO for some
businesses might be inconsistent in some ways with the general FO
-- for example, one might have a 4D and the other a 3D view of time
and space.    (016)

Fortunately, the lattice comes to our rescue by giving us a way to
determine the least common generalization of the general FO with the
incompatible SFO.  That common generalization defines the areas on
which interoperability is possible.    (017)

AH> I agree the two approaches aren't conflicting, i just wanted
 > to emphasize that an FO is NOT NECESSARY for large scale
 > interoperability. It might be useful, but it is not necessary.    (018)

I agree.  Pat has high hopes that an outstanding FO might someday
be discovered.  There's no harm in searching for it.  But the most
likely place to find it is among the theories in the hierarchy.    (019)

So far, the best recommendation is to consider the FO as a theory
that has been awarded a gold medal for success in some competition.
And the best competition is the marketplace of ideas:  Is there
some common generalization in the hierarchy of theories that has
proved to be fruitful for spawning more specialized theories
for a wide range of applications?    (020)

MB> Perhaps some other model relationship, other than generalization
 > / specialization, is needed for ontology interoperation.    (021)

Another operator is what I call analogy:  taking one theory and
renaming some of the labels (i.e. names of relations, types, or
individuals) to create another theory that is isomorphic with
the first.    (022)

For examples, see Figure 4 near the end of the following paper:    (023)

    A dynamic theory of ontology    (024)

John    (025)

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