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A simple example of an IRI denoting different resources in different graphs

From: David Booth <david@dbooth.org>
Date: Fri, 13 Dec 2013 13:37:07 -0500
Message-ID: <52AB53D3.7000500@dbooth.org>
To: www-archive <www-archive@w3.org>
Here is a simple proof that "Two different appearances of an
IRI denote the same resource" is false.

Assume the usual standard namespaces for OWL, etc.
Assume the following example namespace:
   @prefix ex: <http://example/>

Let G1 be the following graph:
  { ex:monument owl:sameAs ex:statueOfLiberty . }

Let G2 be the following graph:
  { ex:monument owl:sameAs ex:eiffelTower . }

Now, the formulas in the RDF Semantics allow the truth value
of any graph to be determined with respect to (WRT) any interpretation. 
  Nothing in the spec restricts the choice of
graph whose truth value may be determined, nor does it
restrict the choice of interpretation under which that truth
value may be determined.  So . . .

Let I1 be the following interpretation:
  { owl:sameAs         -> the standard owl:sameAs relation;
    ex:statueOfLiberty -> The Statue of Liberty;
    ex:eiffelTower     -> The Eiffel Tower;
    ex:monument        -> The Statue of Liberty;
    for every other URI u, u -> u, as in a Herbrand interpretation.
  }

Let I2 be the following interpretation:
  { owl:sameAs         -> the standard owl:sameAs relation;
    ex:statueOfLiberty -> The Statue of Liberty;
    ex:eiffelTower     -> The Eiffel Tower;
    ex:monument        -> The Eiffel Tower;
    for every other URI u, u -> u, as in a Herbrand interpretation.
  }

Now, suppose we use the RDF Semantics to determine the truth
value of G1 WRT I1.  To do so, we substitute G1 and I1 into
the semantic formulas and examine the result.  In this case,
the formulas tell us that G1 is true, and we notice that they
constrain ex:monument to denote The Statue of Liberty
everywhere it occurs in G1.

Furthermore, suppose we also use the RDF Semantics to determine
the truth value of G2 WRT I2.  Similarly, we substitute G1 and
I1 into the semantic formulas and examine the result.  In this
case, the formulas tell us that G2 is true, and we notice that
they constrain ex:monument to denote The Statue of Liberty
everywhere it occurs in G2.

Now, notice that:

  - ex:monument appears in G1 and it appears in G2, and these
are different appearances;

  - The Statue of Liberty is not the same resource as the Eiffel
Tower; and

  - ex:monument denoted a *different* resource in G1 than it
denoted in G2 (because different interpretations were
applied to G1 and G2).

This example has shown a case in which two different appearances of an 
IRI have denoted different resources.  Therefore, the statement that 
"Two different appearances of an IRI denote the same resource" is false.

David
Received on Friday, 13 December 2013 18:37:36 UTC

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