Patrick, Matthew, and Steve, (01)
If by continuum, you mean something that is continuous,
then the answer is no because ontologies contain a discrete
set of types and statements. (02)
PD> I am concerned with the suggestions that it is possible to
> create a continuum along which to organize what are known
> as "ontologies" in one or more circles. (03)
But if you want to relate one ontology to another, there is
indeed a very systematic way of doing so: a lattice.
But a lattice is not one-dimensional. (04)
Every ontology is a theory, which consists of a collection
of predicates that represent the types of entities that
are considered in that ontology and a collection of axioms
that state definitions and constraints that must be true
of those predicates. (05)
About 70 years ago, Adolf Lindenbaum observed that such a
collection of theories forms a lattice. The partial ordering
of theories is defined by generalization and specialization.
A theory T1 is more general than T2 iff T1 is true of more
cases or states of affairs than T2. (06)
Every formal ontology that has ever been defined or ever will be
defined -- whether good, bad, or indifferent -- fits somewhere in
that lattice. Every informal ontology, as soon as it is stated
in a some version of logic, becomes a formal ontology and it also
has a place somewhere in that lattice. (07)
SR> I would remind everyone that we are not trying to judge
> the quality or usefulness of the ontology - we're trying to
> categorize what "kind" of ontology something is. (08)
The lattice says nothing about quality. But it does show which
ontologies are specializations of others. If you give some
general examples of each "kind" of ontology, everything that is
a specialization of one of the general kinds is of the same kind. (09)
MW> If we were really talking about "kind", we probably ought
> to be back to talking about 3D and 4D again... (010)
3D and 4D theories are examples of kinds, and you could formulate
a very simple, but general ontology of either kind. Then each
of them would have all others of that kind as specializations.
But there would also be many different "subkinds" and various
"kinds" determined by other distinctions. (011)
John Sowa (012)
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