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Re: [ontolog-forum] standard ontology

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Wed, 11 Feb 2009 21:43:47 -0500
Message-id: <49938CE3.7000100@xxxxxxxxxxx>
Ali,    (01)

The ultimate goal is unattainable:  an infinite lattice of all possible
theories.  Even for a finite hierarchy, it's not easy to detect all
possible links and equivalences.  Therefore, I suggest a more modest
project of building a hierarchy incrementally with as many links as
anyone has found at any given stage.  It is, of course, desirable
to find and document as many links as possible, but an incomplete
hierarchy is far better than an unordered registry.    (02)

 > 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.    (03)

Certainly.  But I wouldn't expect everyone who contributes an
ontology to the registry to be able to detect and prove all
possible combinations before submitting it.    (04)

 > 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?    (05)

Two provably equivalent axiomatizations should be recognized
and documented as equivalent ways of stating the same theory.
But again, I wouldn't require anyone to search for and prove
every equivalence before submitting an ontology.    (06)

Furthermore, I would *encourage* people to subdivide ontologies
into smaller, reusable modules.  But I would not require anyone
to do so as a prerequisite.  If anyone finds it useful to do
the subdivision, they could register all the modules, the manner
of derivation, and the reason why such a subdivision may be useful.    (07)

 > 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?    (08)

The question of what is an ontology is controversial.  I would use
the term 'module' or 'theory' for each entry in the registry, and
people could call them ontologies, if they like.  I would not set
any lower bound on the size of a module.  (The empty module at
the top, for example, has zero axioms.)    (09)

 > 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....    (010)

There is no reason why there couldn't be an open-ended number
of ways of organizing and relating the modules.  All the possible
links that have been found could be documented in the metadata,
and new kinds of metadata could be added whenever anyone finds
a use for them.  A module browser could highlight or suppress
any links that anybody might want to see or ignore.    (011)

 > 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)    (012)

I agree.  I prefer the terms 'infimum' and 'supremum' because
it's easier to remember which one is above and which one is below.    (013)

The important point is that the registry should contain metadata
about relationships among the modules.  That enables all current
ontologies (Cyc, SUMO, DOLCE, BFO, etc., etc.) to be registered,
and people can begin dissecting them, recombining parts, and
recording as many relations as they can find among them.    (014)

As an example of the kind of processing that can be done, I
recommend the following paper (which I've cited many times):    (015)

    Peterson, Brian J., William A. Andersen, & Joshua Engel (1998)
    "Knowledge bus: generating application-focused databases from
    large ontologies," Proc. 5th KRDB Workshop, Seattle, WA.
    http://sunsite.informatik.rwth-aachen.de/Publications/CEUR-WS/Vol-10/    (016)

They used Cyc as a development tool, from which they extracted
about 5,000 axioms that they needed for their application.
Lenat didn't approve of that project, because he didn't want
to encourage people to run Cyc axioms on other systems.    (017)

I believe that was a major blunder, because Lenat could have
started a profitable business built on using Cyc as a resource
for developing axiom sets that could be used in a wide variety
of other systems -- including any kind of database, expert system,
or the Semantic Web.    (018)

John    (019)

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