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Re: RDF semantics: a question about instances and interpolation lemma

From: pat hayes <phayes@ai.uwf.edu>
Date: Tue, 3 Dec 2002 10:44:18 -0600
Message-Id: <p05111b0aba128e26a0e0@[]>
To: Chet Murthy <chet@watson.ibm.com>
Cc: www-rdf-interest@w3.org

>[Not sure if this is the right place to send such a note.]
>I was reading RDF-MT (http://www.w3.org/TR/2002/WD-rdf-mt-20021112/)
>and it seems to me that there's a problem with the definition of
>instances.  This might be trivial, and just an ambiguity in the spec.
>Definition of instance:
>An instance of an RDF graph is, intuitively, a similar graph in which
>some blank nodes may have been replaced by urirefs or
>literals. However, it is technically convenient to also allow blank
>nodes to be replaced by other blank nodes, so we need to state this
>rather more precisely. Say that one triple is an instance of another
>if it can be obtained by substituting zero or more urirefs, literals
>or blank nodes for blank nodes in the original; and that a graph is an
>instance of another just when every triple in the first graph is an
>instance of a triple in the second graph, and every triple in the
>second graph has an instance in the first graph. Note that any graph
>is an instance of itself.
>By this definition,
>(1a) eg:a eg:prop1 eg;b.
>(1b) eg:c eg:prop2 eg:d.
>is an instance of
>(2a) _:a eg:prop1 _:b.
>(2b) _:b eg:prop2 _:c.
>(1a) is an instance of (2a) by { _:a -> eg:a, _:b -> eg:b }
>(1b) is an instance of (2b) by { _:b -> eg:c, _:c -> eg:d }
>Clearly, this shouldn't be allowed, but I can't find a reading of the
>definition of instance which disallows it.  Equally, the model theory
>seems to indicate (I haven't worked thru the details completely) that
>this entailment should NOT hold.

Right, it should not.

>I think I could formulate a modified definition of instance, to
>restore the Interpolation Lemma, but, well, I figured I'd check and
>see if I was barking up the wrong tree ...

No, good tree, good bark. You are right, and this needs fixing. 
Please by all means send any suggestions you have. Here's mine, which 
is traditional but whose complexity I had hoped to avoid:

An instance mapping is a function from bnodes to (bnodes union 
literals union urirefs) ; an instance of a graph G under the mapping 
M is the result of replacing every bnode subject or object x in G by 
M(x) . An instance is an instance under some mapping.

Pat Hayes


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Received on Tuesday, 3 December 2002 11:43:56 UTC

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