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

From: Richard Fikes <fikes@KSL.Stanford.EDU>
Date: Tue, 18 Sep 2001 11:38:56 -0700
Message-ID: <3BA794C0.72D29798@ksl.stanford.edu>
To: Sandro Hawke <sandro@w3.org>
CC: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>, 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

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.

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.  (And I think Richard
Waldinger and I have worked out a viable solution to the problems
involving cardinality constraints also, but we shall see.)

Hope this helps.

Richard
```
Received on Tuesday, 18 September 2001 14:41:33 UTC

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