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RDF graph equality

From: <herman.ter.horst@philips.com>
Date: Thu, 6 Feb 2003 20:03:19 +0100
To: www-rdf-comments@w3.org
Message-ID: <OFD0747BAA.1AA688F1-ONC1256CC5.00392C42-C1256CC5.0068D826@diamond.philips.com>
I agree with and would like to expand on Dan Connolly's 
remark about RDF graph equality.

The RDF Concepts and Abstract Syntax document defines
RDF graphs to be sets of triples. 
In this way, equality of RDF graphs is also defined.
Namely, by one of the first axioms of set theory, two
sets are equal if and only if they have the same elements.
Therefore, the definition of RDF graph equality given in the
Concepts document would introduce contradictions:
two RDF graphs which do not have exactly the same
triples may be equal and not equal at the same time.

Equivalence would indeed be a perfect name for the notion
that is defined.  Note that equivalence thus defined 
is an equivalence relation on the class of all RDF graphs.

I can understand the intent behind the word "equal"
in the Last Call RDF Concepts draft.
For many purposes, RDF graphs can be replaced by
equivalent graphs.
A central point that could be noted is as follows:
the truth of any semantic statement involving RDF(S)
(for example an interpretation I satisfies an RDF graph E,
or a set of RDF graphs S entails an RDF graph E),
is not changed when any RDF graph is replaced by
an equivalent graph.

In analogy with many similar situations in various
mathematical theories, it could be said that 
"equivalent RDF graphs are identified", but then
identical cannot be interpreted to be the same as equal.

Herman ter Horst
Received on Thursday, 6 February 2003 14:05:16 UTC

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