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Re: [ontolog-forum] Role of definitions (Remember the poor human)

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Wed, 14 Feb 2007 12:41:41 -0500
Message-id: <45D349D5.8080508@xxxxxxxxxxx>
Pat, Chris, Kathy, and Barry,    (01)

The problem of stating necessary and sufficient conditions
for defining anything is nontrivial, even in mathematics.
For phenomena in nature or the results of typical human
behavior, definitive statements are problematical, to say
the least.    (02)

Belief revision systems, database systems, and knowledge-based
systems distinguish levels of "entrenchment" (whether or not
they use that term), and I believe that an ontology should also
make such distinctions at the metalevel.  Following are some
"levels of entrenchment" in descending order of strength:    (03)

  1. Type hierarchy.  The classical tree or partial ordering
     introduced by Aristotle and first drawn by (or attributed
     to) Porphyry.  It's useful in every field, it's not going
     away, and we should recognize it as the minimal requirement
     for an ontology.    (04)

  2. Necessary distinctions.  The differentiae that split any
     type into two or more subtypes.  If the split is binary
     (A or not-A), then it is both necessary and sufficient for
     distinguishing the two subtypes from one another, but the
     conditions for characterizing the supertype might not be
     necessary and sufficient.    (05)

  3. Constraints.  Additional statements that characterize the
     types or the interactions of entities of various types.
     The constraints are necessary relative to the ordinary
     facts in level #4, but they might not be considered
     defining characteristics.    (06)

  4. Ordinary facts.  Ground-level assertions that must be
     consistent with statements at the above levels, but they
     may violate defaults at level 5.    (07)

  5. Defaults and probabilities.  Statements that are usually
     true of entities of a given type or types, but they are
     at the bottom of the entrenchment pole.  A probable
     statement is a default with an associated value that
     indicates its likelihood or frequency of occurrence,
     given the occurrence of some other condition.    (08)

Systems of entrenchment levels along such lines are widely
used and should be supported.  Cyc, for example, has 3 levels:
True, true by default, unknown (and the negations -- false
by default and false).  But I think that Lenat would agree
that a privileged level should be added for some of the
axioms, especially ones that define the type hierarchy.    (09)

A declaration of which level a particular statement belongs to
would not be part of the first-order theory, but it would be
a metalevel statement that should definitely be considered
part of the ontology.    (010)

John    (011)

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