John,
(Probably off topic) (01)
I am a fan of the lattice, not sure it is the subject of this thread,
but a fan anyway. (02)
And, you can certainly plug any bunch of statements into a node of the
lattice and call it a theory. What I am wondering about is the most
effective organization of the lattice. I have a theory about that
(which you probably have a paper on from 1988) - that theory is that a
node in the lattice should contain all of the facts that have identical
context (apply to the same kinds of situations and situations). This
organizing principle for the lattice would serve to organize the
knowledge, provide for provenance and contextualization, as well as
provide the hook for second order statements - in that they could then
talk explicitly about context by including sets of nodes in the lattice
into other nodes. This should work even in simple logics, like OWL. (03)
Does this fit with your lattice? Or, do you have an organizing
principle for the lattice? (04)
-Cory (05)
-----Original Message-----
From: ontology-summit-bounces@xxxxxxxxxxxxxxxx
[mailto:ontology-summit-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F.
Sowa
Sent: Friday, January 19, 2007 10:21 AM
To: patrick@xxxxxxxxxxx; Ontology Summit 2007 Forum
Subject: Re: [ontology-summit] Defining "ontology" (06)
Patrick, Matthew, and Steve, (07)
If by continuum, you mean something that is continuous, then the answer
is no because ontologies contain a discrete set of types and statements. (08)
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. (09)
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. (010)
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. (011)
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. (012)
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. (013)
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. (014)
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. (015)
MW> If we were really talking about "kind", we probably ought
> to be back to talking about 3D and 4D again... (016)
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. (017)
John Sowa (018)
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