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separating consistency, conformance from the state of the web

From: Dan Connolly <connolly@w3.org>
Date: 29 May 2003 10:56:00 -0500
To: www-webont-wg@w3.org
Message-Id: <1054223759.21361.129.camel@dirk.dm93.org>

Persuant to my action of 8May,

[[
3.2 use of xml:base
...
new ACTION Dan - create a test for this
]]
-- http://lists.w3.org/Archives/Public/www-webont-wg/2003May/0120.html

I'm reviewing the specification of imports,
entailment, consistency and such, and I think
the imports nonsense has leaked into parts of the
spec that we agreed not to let it leak into.
Hmm... no, on review I see that the business about keeping
imports closure separate from entailment never
actually got decided by the WG. In any case...

My understanding of the design was: entailment (and
hence consistency) was defined as a purely mathematical
relationship between graphs, with no dependency on the state of
the web.

Imports closure is a sort of scruffy notion involving
web access.

You can do the scruffy imports closure stuff, take the
resulting graphs, and test them for consistency,
entailment, and all that. But the definition of
entailment and consistency itself doesn't depend
on the state of the web.

This is not the way the specs are written.


One particular problem is this ill-formed
definite description in S&AS:

"the RDF/XML document, if any, accessible at u"
http://www.w3.org/TR/2003/WD-owl-semantics-20030331/rdfs.html#RDF_graph_imports_closure

In the general case, there's more than one RDF/XML document
accessible at u.

That's in the definition of imports closure; I expect
a certain amount of scruffiness there. But the following
definions (from section 4.1. Document Conformance of
the test doc) all depend on it:
  - OWL DL document
  - OWL Lite document
  - consistent OWL Lite/DL document
  - consistent OWL Full document

i.e. deleting document X can cause document Y to cease
to be an OWL DL document.

Also, I think there's a sort error in section 4.1.2. Semantic
Conformance of test: "An OWL Lite or OWL DL document D
is consistent ... if and only if ... such that I
satisfies an abstract ontology O equivalent to D".
D is a document but equivalence is defined over graphs.

I'd rather define conformance independent of the state of the
web; here's an attempt:

  An OWL Full document set is a finite set of RDF/XML documents.

  An OWL Full document set is imports-closed if the corresponding
  set of RDF graphs is imports closed [cf S&AS 5.3].

  An _OWL DL document set_ is an OWL Full document set
  the merge of whose RDF graphs is an OWL DL ontology in RDF graph form.

  An _OWL Lite document set_ is an OWL Full document set
  the merge of whose RDF graphs is an OWL DL ontology in RDF graph form.

  An OWL Lite or OWL DL document set consistent with respect to
  a datatype theory T if and only if there is some abstract OWL
  interpretation I with respect to T such that
  I satisfies an abstract ontology O equivalent to D,
  in which O has a separated vocabulary; and D is the merge
  of the RDF graphs of the document set.

  An OWL Full document set is consistent with respect to
  a datatype theory T, if and only if there is some OWL Full
  interpretation I with respect to T such that I satisfies
  all the RDF graphs corresponding to the documents in the set.

Note that consistency is defined independently of
imports closed-ness.

In fact, since imports closure isn't really formally defined,
I'd prefer to move it out of S&AS altogether. I'm pretty
sure it's not needed there. I'd be happy to see it 
moved to the document conformance section of test.

-- 
Dan Connolly, W3C http://www.w3.org/People/Connolly/
Received on Thursday, 29 May 2003 11:55:40 GMT

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