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Re: [ontolog-forum] Inconsistent Theories

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Tue, 09 Feb 2010 09:32:01 -0500
Message-id: <4B7171E1.6060203@xxxxxxxxxxx>
Rich, Ian, and Chris M,    (01)

The recent discussions in this list indicate how easily verbiage
in ordinary language can be misunderstood.    (02)

Chris and I, for example, have been collaborating on the CL
project for years, and we occasionally have misunderstandings
about the verbiage for talking about the formalism (as in the
previous couple of notes).  But we usually reach an agreement
very quickly about the formal operations and the results they
generate.    (03)

That is why we have put so much emphasis on the need for formal
notations whose semantics is formally specified.    (04)

RC> Value is simply one property of a Thing in a universe.  Identity
 > wrt a Definition property is a complete different issue.  You are
 > confusing a logical specification of value with a logical instance
 > of a value.    (05)

I wouldn't attempt to explicate statements like that.  There are
too many words and phrases that different people could easily
interpret in different ways.    (06)

In a Tarski-style model, there is no talk about "property of a Thing
in a universe".  All you have is a set D called the "individuals",
a set R called the "relations", every relation in R is specified
by n-tuples of entities from D, and there are "assignments" of
elements of D to the "names" in some formal language(s).    (07)

If you don't like the term 'domain', you can say 'universe'.
If you don't like 'individual', you can say 'entity' or 'Thing'.
If you prefer, you can replace the term 'relation' with 'predicate',
or you can use the term 'property' for one-place or one-argument
or unary or monadic relations.  And if you don't like the term
'assignment', you can replace it with 'mapping' or 'association'.    (08)

If there's any confusion about the verbiage, focus on the sets D
and R and their mapping to the formalism.  The sets are critical,
what you call them or their elements (or members) is irrelevant.    (09)

CM>> I have to say again, I don't think there's much practical upshot
 >> here.  Seems pretty unlikely to me that any real world ontology is
 >> going to be interested in declaring that there exists some specific
 >> finite number of things.    (010)

IB> I may have missed the context of this statement, but it seems
 > rather at odds with my experience. Singleton and doubleton classes
 > are not that unusual in ontology, and their membership is finite.    (011)

Yes, the context for interpreting a sentence is another source
of confusion.  In some examples in previous notes, there was
a discussion of a universe or domain D with a fixed, finite number
of elements.  Chris made the point that such a limit is unlikely
in most practical applications.    (012)

But it is also true that the elements of the domain D may frequently
contain small finite sets such as singletons or doubletons, and
the set R of relations will be specified by sets (possibly infinite)
whose elements are finite n-tuples.    (013)

Bottom line:  In order to specify a standard with sufficient precision
that all implementations are exactly compatible, we must use formal
languages whose semantics are specified in terms of formal models.    (014)

John    (015)

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