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Re: [ontolog-forum] Foundation ontology, CYC, and Mapping

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Thu, 04 Feb 2010 09:04:33 -0500
Message-id: <4B6AD3F1.4090302@xxxxxxxxxxx>
Pat,    (01)

Adding more axioms is a change, and it can create inconsistencies
when different people add different axioms.    (02)

JFS>> As soon as you add more axioms to a theory, the "meaning" of the
 >> so-called "primitives" changes.    (03)

PC> I am not certain that that is true.  If one adds subtypes to the
 > types of an ontology, and each subtype has some properties or
 > restrictions not applying to the parent, then it does not seem to me
 > that the *meaning* of any of the parents changes, though we are
 > asserting more information about the properties of the parents
 > (i.e. that some instances have or may have
 > certain properties).    (04)

There are many ways of extending a theory.  What you are describing
is a "conservative" extension, which merely assigns names to
"closed-form expressions".    (05)

But Chris M. used the example of set theory, all versions of which
have the same two "primitives" -- subsetOf and elementOf.  Any
extension that merely gave names to various combinations of those
operators without adding new axioms would be a conservative extension.    (06)

However, the many different versions of set theory have added different
axioms.  All the main theories include finite sets and even countable
sets in compatible ways.  But they differ on the extensions to higher
orders of infinity.  The two basic primitives differ from one version
to the next on those extended branches.    (07)

Since you haven't formalized your system in full detail, it's hard to
say exactly what it would be if fully defined.  But I suspect that
what you have in mind is a closed system:  a finite set of relations
(i.e. primitives) that are fully specified by necessary and sufficient
conditions.  The semantics of those primitives would never change in
any way.    (08)

Then all possible terms that could be defined in your system would
consist of closed-form definitions of the following kind:    (09)

    Every term T is either a primitive or it is defined as synonymous
    to an expression that is composed only of primitives.    (010)

Most systems of mathematics are far more complex than that, and
you couldn't even define the full range of useful physics with such
a limited framework.    (011)

Longman's dictionary seems to work, but only because the definitions
are so vague that they don't constrain the subject matter very much.    (012)

John    (013)

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