Re: [ontolog-forum] standard ontology

[Ali Hashemi <ali.hashemi@xxxxxxxxxxx>]

John,

What you describe resonates a lot, but there are some minor quibbles.

First, by focusing on direct axiom reuse, we may limit ourselves to syntax matching. In my mind, it makes more sense to focus on the models that arise from the axioms as opposed to whether a particular matching axiom formulation has been implemented.

For example, restricted to lattices, the set of models for "meet" and "join" are the same as those for"minimal upper bound" and "maximal lower bound."

I would imagine that we would want this lattice of theories to be able to accommodate these types of equivalences.

Another point - i'm not sure whether you are actually saying this or not, it seems to be implied. But it appears you are suggesting that the level of granularity for "acceptance" as an ontology would be axiom level. 

Imagine I have two modules, in M1 I have two sentences P and Q vs another module M2 where I have the single sentence S = P&Q

Are they two axioms or one? Further might P alone constitute an ontology? What're the criteria for the ontology "worthiness" of an axiom or a set of axioms? Practical use i would guess.

Imagine the first theory i see is that for "addition." It shares nothing with what I want but the property of associativity. Does this suggest that there is a unique theory called "associativity"? Is that an ontology? How exactly does the axiom (module? / ontology?) of "associativity" make sense de-contextualized from it's usual cohort axioms of transitive, reflexive etc.?

--

One practical question is also how to organize the resultant explosion of theories or ontologies.

Instead of organizing all these theories or modules in a single layer or hierarchy, we could go orthogonal. Using planes / layers seem to be a promising way to declutter the combinations and making traversing this "space" more efficient. If we know the content of modules, i.e. these modules are about geometries, these axioms are about mereotopologies, etc. - we might then use representation theorems or mapping axioms, to get us out of a particular plane and into another. We do this since, beyond axiom matching, they establish the semantic equivalence between axiom sets which differ syntactically and possibly even methodologically (mlb vs join). 

Does that make sense? :P

//

Cheers,

Ali

On Wed, Feb 11, 2009 at 8:59 AM, John F. Sowa <sowa@xxxxxxxxxxx> wrote:

Pat,

I agree that we should begin today with a constructive approach:

PC> My difficulty with just waiting until some "large and

 > economically important community of practice" evolves is, that
 > on the basis of the experience of the past fifteen years, this

 > process could take several decades, or longer....

My recommendation is to begin with a registry and a methodology
for using metadata to show the generalization hierarchy among
theories.  I outlined a 4-point procedure for doing that.
(See the copy below.)

To illustrate that procedure, I'll pick some random names for
hypothetical ontologists.  Let's suppose that somebody, Azamat,
contributes ontology A to the registry, and Ian contributes
ontology I.  Then we have a hierarchy with the empty ontology E
at the top and with two branches from E to A and from E to I.

Then suppose that another ontologist, Xavier, examines A and I,
likes some aspects of each, but finds other parts of each that
are incompatible.  So Xavier extracts the axioms he wants from
A to form a new ontology AX, which is a generalization of A
(because the axioms of AX are a proper subset of A).  Therefore,
the new ontology AX resides along a branch from E to AX to A.
Then Xavier extracts some axioms from I to form IX, which is
a generalization of I along the branch from E to IX to I.

Finally, Xavier checks whether the conjunction of AX&IX is
consistent.  To do that, he tests the axioms against his
favorite domain D to check whether all the axioms of AX&IX
are true of D.  If so, AX&IX has at least one model and must
be consistent.  Then Xavier registers all three ontologies
AX, IX, and AX&IX in the registry together with the metadata
about how they were constructed, tested, and used.

Later, another ontologist, Yolanda, browses through the registry
and chooses AX&IX for her project.  She decides to add more
axioms Y to form a new ontology AX&IX&Y, which she registers.

Then Zachary decides that AX&IX is useful for his project, but
he needs to add some axioms that are inconsistent with Y.  So
he forms an ontology AX&IX&Z, which he puts in the registry.

Another ontologist, Winnie, studies the additions Y and Z
and discovers that they have a useful common generalization,
which she calls W.  So Winnie registers AX&IX&W as a new
specialization of AX&IX and a common generalization of
AX&IX&Y and AX&IX&Z.

The method of registration and revision has proved to be very
effective for the open-source software community.  The major
addition for ontologies is the requirement that the metadata
explicitly show the complete path of generalizations and
specializations that were made to derive the ontologies.

The generalization hierarchy of ontologies is nothing more
nor less than a record of all the derivations made during
the development stages *PLUS* any additional observations
(such as Winnie's discovery of a common generalization).

John
_________________________________________________________________

[Extract from a note, subject line, An Ultra High Level Ontology,
by J. F. Sowa, dated 10 Feb 2009, at 6:50 PM, Eastern US Time.]

My basic proposal, which I have been repeating in different ways
for many years, is extremely simple:

 1. Set up a registry for ontologies with minimal requirements
    for contributions and some basic reviewing for competence.

 2. Emphasize that ontologies should be constructed from modules,
    and multiple use and reuse of other modules in the registry
    should be strongly encouraged.

 3. The sequence of uses and reuses would automatically create
    a generalization hierarchy of ontologies -- i.e., if ontology
    X incorporates the module Y, then X is a specialization of Y.

 4. Any collection of modules that are frequently used and reused
    would be high up in the generalization hierarchy, and they
    would also become prime candidates for being "canonized" as
    the recommended subset for further use and reuse.

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