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Re: [ontolog-forum] Constructs, primitives, terms

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Thu, 08 Mar 2012 11:16:09 -0500
Message-id: <4F58DB49.9050202@xxxxxxxxxxx>
Paul,    (01)

I'll try once more to explain the problems that URIs and shared
definitions, by themselves, cannot solve.    (02)

>> Everybody agrees that globally unique IDs are useful.  But they are
>> not magic.    (03)

> Agreed. I never said they were--only that they were a better investment.
> My only claim is that if you use URIs consistently for referring to
> things, and RDF consistently for making assertions about things, you
> have an easy road to improved communication.    (04)

Yes.  My only claim is that nobody disagrees with that.    (05)

> I admit I am stumped by "using a vocabulary in different contexts".
> Perhaps you mean "with a different set of axioms"? If we agree to say
> "ex:foo", but you put it in play with different axioms than I do, we
> haven't gained anything.    (06)

I'll use ordinary logic to describe the issues, but you can translate
the description to OWL or any other version of logic anyone may prefer.    (07)

  1. Let's suppose we have a set of globally unique terms, each of which
     has a URI that specifies a precise definition.  The collection of
     all those definitions can be called the global theory G.  And let's
     assume that G is consistent -- i.e., no implied contradictions.    (08)

  2. Logicians show that any consistent set of definitions has one or
     more models.  Those models correspond to various applications of G
     for different purposes.  Every statement that can be said about any
     such model is guaranteed to be consistent with G.    (09)

  3. But two independently developed applications, say A and B, may add
     new information in addition to the common definitions in G.  I'll
     call the information added to A or B the "local context" of A or B.    (010)

  4. Let's assume that all the local applications have been thoroughly
     debugged so that G plus each local context is consistent.  In terms
     of model theory, that implies there exists one or more models for
     that application, which are also among the models for G.    (011)

  5. Unfortunately, there is no guarantee that all the models for
     any theory G are consistent with one another.  Two applications
     A and B that are each consistent with G can have info in their
     local contexts that conflict with info in the other's context.    (012)

  6. If we are lucky, that additional information might only create
     contradictions that involve local terms so that any statements
     that are limited to using terms in G can be shared among A and B.    (013)

  7. Unfortunately, Murphy's Law still applies.  The new info in the
     local contexts may create inconsistencies between A and B that
     use only the terms defined in G.  Some statements may be true in
     A, but false in B, *even though* they don't use any local terms.    (014)

> Then if you say "ex:foo rdf:type ex:baz.", which is unexpected
> in my  "context", I will ask what you mean by that, and we will
> get even farther along.    (015)

But point #7 implies that contradictions can arise even if there are
no unexpected terms with unexpected definitions.    (016)

For example, suppose both systems use the same definitions for the
terms 'person', 'employee', and 'age'.  And let's assume that they
also have copies of the same government rules and regulations.
But company A has a rule that all employees must be over 18, and
company B says that all employees must be over 21.    (017)

Then company A sends B the message "Person George is an employee."
Then B concludes that George is over 21.  That can create a problem
if George is only 19 and he's hired as a bartender.    (018)

If you think that B should check George's age before hiring him,
let's suppose that company A is a catering service, and B requires
caterers to pour drinks.  In that case, B doesn't directly hire George,
but a conflict arises in the task that George does while employed by A.    (019)

The number of possible conflicts is infinite, and no fixed set
of universal definitions can anticipate and rule out all of them.    (020)

John    (021)

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