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Re: Making Rules Out of RDF-Graphs (Re: What is an RDF Query?)

From: Pat Hayes <phayes@ai.uwf.edu>
Date: Wed, 19 Sep 2001 10:42:14 -0500
Message-Id: <p05101012b7ce6bd41de3@[205.160.76.182]>
To: Richard Fikes <fikes@ksl.stanford.edu>
Cc: www-rdf-rules@w3.org
>  > Anyone out there psyched to axiomatize
>>  RDFS?
>
>As both Peter and Pat have said, the paper "An Axiomatic Semantics for
>RDF, RDF Schema, and DAML+OIL"
>(http://www.ksl.stanford.edu/people/dlm/daml-semantics/abstract-axiomatic-semantics.html)
>contains an axiomatization of RDF and RDF-S in first order logic. Here
>are some comments about that axiomatization related to this e-mail
>thread.
>
>Regarding "holds".  We did not use "holds" in the axiomatization because
>of various concerns about the semantics of "holds" and whether it is
>legitimately within FOL.  However, we achieved the desired effect of
>"holds" by not assuming that RDF properties are relations.  We, instead,
>use the relation "PropertyValue" for all RDf statements and provide it
>with three arguments, a property, an object, and a value.

This is really 'holds' with another name :-). The model theory for 
RDF makes a similar assumption, by the way, by distinguishing between 
a property and its relational extension. PropertyValue (P O V) is 
encoded as EXT(P)(O V) where EXT is the extension mapping.

>Regarding Horn logic.  I don't think our axioms for RDF and RDF-S can be
>stated in Horn Logic.  We made no attempt to do that.  My opinion is
>that it would be difficult or perhaps even impossible to axiomatize RDF
>and RDF-S in Horn logic.  We have, however, included in the document a
>set of "theorems", all of which are either expressible in Horn Logic or
>conclude "false" from a conjunction of RDF statements.  Those "theorems"
>do not provide a logically complete axiomatization of RDF, RDF-S, or
>DAML+OIL.  However, they cover a sufficiently large portion of the
>semantics of each language, that a reasoner that uses only them may have
>significant usefulness in Semantic Web applications.
>
>Pat mentioned problems regarding the use of KIF for the axiomatization.
>To my knowledge, the only open problems in that regard involve the
>axiomatization of the cardinality constraints in DAML+OIL, and so are
>irrelevant to the axiomatization of RDF and RDF-S.

I agree with that, and apologize for bringing the issue up. The only 
way it could be relevant to RDFS is if RDF decided that containers 
could only have finitely many members and wanted to be able to 
represent that restriction; but that isn't likely to happen.

Pat


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Received on Wednesday, 19 September 2001 11:42:18 GMT

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