Those are good points. Since we would like to have systematic principles
for defining ontologies, we should at least be systematic about our
metaontology for defining ontologies.
>You define TERMINOLOGICAL ONTOLOGY to be neutral with respect to how many
>axioms are in it, but you overload your use this term referring to this
>meaning as well as another kind of ontology which you have not given a name
>i.e. one with few axioms and many terms. This is confusing.
The number of terms and axioms is not the defining criterion. I merely
observed that current ontologies that have lots of terms tend to have few
axioms and vice-versa. But Cyc is an example of a system that is trying
to maximize both.
>I suggest that you use ONTOLOGY for the more general term, and TERMINOLOGICAL
>ONTOLOGY for the latter.
But we would also like to use the term _ontology_ as an inclusive term for
informal ontologies that don't even include a type hierarchy. We have to
choose a selection of terms that (a) correspond roughly to the vague
terminology that is current in the field, (b) include all the options
that are currently being used by various groups, and (c) are defined by
formal distinctions that establish some precise criteria for their use.
At the beginning of that list of principles, I defined an ontology as
"a catalog of the types of things that are assumed to exist in a domain
of interest D from the perspective of a person who uses a language L
for the purpose of talking about D."
This definition does not presuppose any formal organization or axioms
of any kind. I think that we should keep it that broad, because there
are many kinds of lists and catalogs that serve as resources for further
analysis and formalization.
Then we have things like WordNet, which are organized primarily by a
partial ordering of _synsets_, which correspond to concept types
in a generalization/specialization hierarchy. WordNet does include some
other relations, such as part-whole, but those are not developed in
as much detail.
Another family of formalisms includes the KL-ONE-like systems, which
are much more formal (and usually smaller) than WordNet. They are now
being called _description logics_, but they used to be called _terminological
logics_. WordNet and similar systems could be formalized with the basic
subset of FOL used in description logics, so the word _terminological_ could
be used to cover both -- KL-ONE-like languages and systems like WordNet
that contain much larger volumes of terms with (at least currently) less
formality in their definitions.
Another basic distinction is the T-box (terminological hierarchy) and
the A-box (assertional system), which has been used in KL-ONE-like systems.
John McCarthy was objecting that there has been "too much emphasis" on the
hierarchy and not enough emphasis on axioms for relations other than subtype.
I agree that we should support both, and I was looking for some term that
would include an A-box with more axioms as a supplement or extension to
a T-box.
But there are also a lot of people in AI and related fields who believe
that prototypes are more flexible for defining terms in areas that are
not as highly formalized or formalizable as mathematics & physics.
There are a lot of philosophical positions that one could adopt about
this point -- i.e. whether that prototypes are essential or whether they
are a methodological expedient for subjects that have not yet been
fully analyzed and axiomatized. I would prefer to avoid that issue
by allowing prototypes as an alternative to an axiomatized A-box.
These distinctions give us a tree (drawn on its side because of limitations
in the typing) somewhat like the following:
Ontology --- Informal Ontology
\
- Terminological Ontology --- Axiomatized Ontology
|
|- Prototype-based Ontology
\
- Mixed Ontology
Where the mixed ontologies may have some branches defined by formal
axioms while other branches are defined by prototypes. The vocabularies
of natural languages tend to be mixed.
The terms that I defined in that list are ones that were tossed around
during the past two years without any definitons. I won't claim that
those definitions I circulated are ideal, so the case is still open
for more revisions, refinements, and extensions. But I think that
we should at least include the kinds of ontologies in that little
tree above, with whatever terms we can agree on.
John