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Re: problems with simple entailment rules

From: pat hayes <phayes@ihmc.us>
Date: Tue, 5 Aug 2003 10:55:50 -0500
Message-Id: <p06001a06bb557b682c1f@[10.0.1.3]>
To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
Cc: www-rdf-comments@w3.org

>I believe that there is a problem with the definition of ``allocated to''
>in the simple entailment rules.  The definition currently (as of the 31
>July version) states
>
>	The terminology 'allocated to' means that the blank node much have
>	been created by an earlier appliation of the specified rules on the
>	same URI reference or literal, or if there is no such blank node
>	then it must be a 'new' node which does not occur in the graph.
>
>My reading of this is that the following RDF graph
>
>	<ex:a> <ex:p> <ex:b> .
>
>cannot be expanded to
>
>	<ex:a> <ex:p> <ex:b> .
>	<ex:a> <ex:p> _:a .
>	<ex:a> <ex:p> _:b .
>
>using the simple entailment rules because once there is a blank node
>created from <ex:b> then all subsequent rule applications must use that
>blank node for <ex:b>.

That is correct. This construction was adopted in order to make 
closures be finite under these rules, and because this restricted 
version is sufficient to produce the required completeness result for 
the vocabulary entailments.  As the text notes, a modification of the 
rule which allows bnodes to be allocated to other bnodes would allow 
this inference and would be complete. The text states this explicitly 
(last para section 7.1):
"These rules will not generate all graphs which have the original 
graph as an instance, which could include arbitrarily many blank-node 
triples all of which instantiate back to the original triples. 
Modifying the rules so that new blank nodes could be allocated to 
existing blank nodes would generate all such graphs. "

>
>Also
>
>	<ex:a> <ex:p> _:a .
>
>cannot be expanded to
>
>	<ex:a> <ex:p> _:a .
>	<ex:a> <ex:p> _:b .
>
>because se1 requires that the object of the triple be a URI reference or
>literal.

Indeed; see comment above.

>This means that the simple entailment rules are not a replacement for the
>instance relationship, which counters the claim in Section 7.1.

What claim?

>  Nor are
>the simple entailment rules complete for simple entailment, which, by the
>way, is not stated in the document.

I am not sure what you mean. The document does not state that the 
simple entailment rules are complete for simple entailment, because 
that would be false: they are not complete (a complete set of rules 
would require an explicit conjunction-elimination rule, for example). 
In fact the text makes clear the way in which they are incomplete, 
and does not state a completeness result.

>Nor are the simple entailment rules equivalent to the alternative rule
>formulation in the second-last paragraph of Section 7.1, as this
>alternative formulation admits the first expansion above.

They are equivalent, and it does not admit that expansion.

>Nor is this
>alternative rule formulation a replacement for the instance relationship,
>as it does not admit the second expansion above.

It is not stated to be so.

As far as I can determine, your message does not indicate any actual 
problems with the entailment rules: you re-iterate several points 
already made in the text and observe that some other points, not made 
in the text, would be false if they were made there. As there is 
nothing here I can find that indicates that there is anything wrong 
with the text, I propose to ignore this message.

Pat
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Received on Tuesday, 5 August 2003 12:18:34 GMT

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