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Re: revised version of semantics document

From: Jos De_Roo <jos.deroo.jd@belgium.agfa.com>
Date: Thu, 22 Aug 2002 15:08:24 +0200
To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
Cc: www-webont-wg@w3.org
Message-ID: <OF910413BF.F7962AA7-ONC1256C1D.0047E4B7@agfa.be>


> Why should anyone care at all about the entailment rules?


Model theory is usually most relevant to implementation
via the notion of entailment, described later, and by
making it possible to define valid inference rules.

Rather than develop a separate theory of the syntactic
conditions for recognising entailment for each reserved
vocabulary, we will use a general technique for reducing
these broader notions of entailment to simple entailment,
by defining the closure of an RDF graph relative to a set
of semantic conditions. The basic idea is to rewrite the
semantic conditions as a set of syntactic inference rules,
and define the closure to be the result of applying those
rules to exhaustion. The resulting graphs will contain RDF
triples which explicitly state all the special meanings
embodied in the extra semantic conditions, in effect
axiomatizing them in RDF itself. A graph rdf-entails
(rdfs-entails) another just when its rdf-closure
(rdfs-closure) simply entails it.

The notion of closure used here is purely a formal device 
to relate two notions of entailment. We do not mean to
suggest that closure rules should be used as a computational
technique, or that actually generating the full closure
would be the best process to use in order to determine
vocabulary entailment. Implementors who wish to check any
kind of entailment should use a process which is optimised
for the combinatorics of the particular set of use cases
that are most likely to arise in a given application area.
In many cases it may be more efficient to use a process
of backchaining on the closure rules, for example.

4.3 A note on computing and entailment

As noted earlier, we do not intend to suggest that these
closure rules be used directly in this form as a mechanism
to compute rdfs entailment between graphs. They are intended
only as a formal specification of a syntactic criterion
corresponding to rdfs entailment. Taken together with the
interpolation lemma for simple entailment, however, they
do define a search space within which a computational system
could find proofs of rdfs-entailment between graphs.

The exact computational significance of finding such a proof
is not determined by the proof itself. For example, one view
of domain and range assertions is that they should be viewed
as constraints on the legality of assertions involving a
property. On this view, the rules rdfs2 and rdfs3 would be
most naturally seen as applying 'backwards', and rdfs2 would
be better phrased as 'If aaa [rdfs:domain] zzz , then if xxx
is NOT [rdf:type] zzz, then xxx aaa yyy is illegal', and
similarly for rdfs3. However, this is the same inference,
differently phrased, as that expressed by the rules in the
table above. In other words, these rules should not be read
as defining only a left-to-right inference pattern. The
entailments they define can be 'used' in any direction by
an inference engine, depending on what its task or purpose
is. All that the model theory defines is the fact of entailment
or non-entailment between RDF(S) expressions. What use is made
of that fact of entailment is up to the particular application.
-- http://www.w3.org/TR/2002/WD-rdf-mt-20020429/Overview.html

and they are on the the web

-- ,
Jos De Roo, AGFA http://www.agfa.com/w3c/jdroo/
Received on Thursday, 22 August 2002 09:09:00 GMT

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