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Re: [ontac-forum] Working with multiple inconsistent theories

To: ONTAC-WG General Discussion <ontac-forum@xxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Fri, 23 Jun 2006 22:55:35 -0400
Message-id: <449CA9A7.1030806@xxxxxxxxxxx>
Leo,    (01)

At that level of generality, we agree:    (02)

 > Many of us agree that we need to use mutually inconsistent
 > theories and yet combine some sub-portions of them to form
 > a consistent working theory/theories.    (03)

But the following point is independent of the above:    (04)

 > However, to go from that statement to the statement that
 > there is thus a need only for informal terminologies and
 > taxonomies except for specialized subsystems does not follow.    (05)

As I've said many times, it would be very nice to have a
reasonably well axiomatized upper-level *if* such a thing
could be found.  I also believe that it is useful to search
for such a thing.  And I believe that the idea of developing
a hierarchy of theories, all cataloged in a metadata registry
is the best way to work toward such an upper level.    (06)

But I would also like to point out the following facts:    (07)

  1. There are many inconsistent proposals for upper levels,
     but no good ways of judging which, if any, is best.
     And none of the people who have upper levels show any
     willingness to abandon their own pet version in favor
     of anybody else's.    (08)

  2. The largest formal ontology in existence is Cyc, and
     nothing else comes close to it in size, number of axioms,
     and years of development effort.  When Lenat says that
     the upper level is not as important as the middle and
     lower levels, you can't dismiss that point without very
     solid evidence to the contrary -- and so far, none has
     been forthcoming.    (09)

  3. Furthermore, there are good reasons for keeping empirical
     axioms out of the upper levels, and leave only definitional
     statements that are true by convention.  For example, I
     would cite "All humans are animals."  I would say that is
     true by convention, because if any humanlike nonanimal were
     ever found, it would be classified as an alien or android.    (010)

  4. Any other empirical facts in an upper level are questionable,
     such as humans have two eyes, ears, arms, and legs, because
     there are many humans who are born with more or less than 2
     of each or who have lost them later in life.    (011)

  5. You could go down to very detailed DNA-like axioms, but
     then you'd get far more detail than is needed for 99.9%
     of all applications.  Therefore, I claim that there is no
     need to have an agreed definition of human other than the
     flat, conventional definition, "a member of the species
     Homo Sapiens".  Any application that needed more detail
     could specify Homo Sapiens in a specialized microtheory.    (012)

  6. If you have any example of an empirical axiom that you
     believe should be in the upper levels, please show me.
     I claim that similar arguments can be found for excluding
     it and any similar axioms from the upper levels.    (013)

 > How about a set of precise mutually inconsistent theories at
 > the upper/middle,domain level from which you can project subsets
 > to form consistent theories -- when you need the precision.    (014)

That's what I've been proposing for years.  It's called the lattice
of theories, of which some finite subset is cataloged in a metadata
registry.  That registry could also contain very big theories, such
as SUMO or Cyc, and very lightweight hierarchies with very few
axioms (except for definitional ones, as discussed above).    (015)

The best way to develop any kind of standard is to allow people
to "vote with their feet":  put all the theories in a metadata
registry, let people pick and choose what they want, and sit
back and see what patterns of usage emerge.    (016)

John    (017)

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