Re: RDF Semantics: corrections

>From: pat hayes <phayes@ihmc.us>
>Subject: Re: RDF Semantics: corrections(was: Re: RDF Semantics: two 
>issues, connected to OWL)
>Date: Tue, 13 Jan 2004 12:41:33 -0600
>
>>  Gentlemen:
>>
>>  Herman has suggested making a change to the wording of the definition
>>  of D-interpretation for the RDF spec., and I would like to make the
>>  change he suggests. The only substantive aspect of this change which
>>  may effect OWL is that in RDF, D-interpretations would no longer be
>>  required to interpret the class extension of the datatype name as
>>  being identical to the value space of the datatype (instead, it could
>>  be a subset

or indeed a superset

>of that class extension.) This would allow a datatype
>>  completeness lemma to be proved for RDFS with datatypes. Herman
>>  suggests that a single sentence can be added to the OWL spec so as to
>>  ensure that this proposed change will not affect the OWL semantics. I
>>  am anxious to ensure that this would be acceptable to the OWL mavens.
>>  Peter and Jeremy, would this proposed change be acceptable to you?
>
>Not without some good indication of why the change is being proposed for
>RDF and what effect it would have on RDF.

The only effect on RDF(S) would be to make it possible to state and 
prove a complete set of rules for D-entailment. None of the RDF(S) 
test cases would be effected.

For clarification, my question to you was concerned with the effects 
on OWL rather than on RDF as such. I was not meaning to ask your 
opinion on the change in a general sense: as indicated, I will take 
responsibility for that. I was asking you only to give an opinion on 
whether the suggestion made by Herman for a 'protective' modification 
to the *text* of the OWL document is indeed sufficient to ensure that 
the RDF and OWL specs, with these changes, will still be compatible. 
The intention is that this will make no change to OWL itself.

>The comment about being able to
>prove a new lemma for RDF with the change indicates that there will be some
>substantive effect to the change.

We do not plan to actually state this lemma in the spec, note.

The substantive change is that, as noted above, the class extension 
of a datatype name is required to contain only the denotations of 
typed literals in the vocabulary, rather than required to *be* the 
value space of the datatype. This brings D-interpretations in line 
with the way that XML typed literals are treated in the RDF 
semantics, which imposes no explicit requirements on 
ICEXT(I(rdf:XMLLiteral))

The only example I am aware of which makes the change visible is this:

ex:a ex:p "true"^^xsd:boolean .
ex:a ex:p "false"^^xsd:boolean .
ex:c rdf:type xsd:boolean .

  |=?=

ex:a ex:p ex:c .

With the current semantics, this is valid (there are only two items 
in the class extension xsd:boolean,  and so ex:c must denote one of 
them); with the proposed change, it is not valid (since the class 
extension of xsd:boolean might consistently contain other items in 
some interpretations.) In general, the changed semantics requires 
that typed literals be classified appropriately, but it does not 
require that class names denote class extensions 'exactly', since any 
such requirement will break simple Herbrand completeness.

Other examples of a similar kind could be given for any finite 
datatype class, of course.

The 'philosophy' behind the change is that an RDFS interpretation 
should only place semantic conditions on items in its vocabulary, and 
that entailments from sets of RDF triples should be consequences of 
information expressed explicitly in those triples. This includes 
typed literals, so that (if you will permit me the luxury of 
including literals as subjects for the moment) it ought to be (and 
is) true that

"foo"^^ex:dtype type ex:dtype .

whenever "foo" is lexically well-formed for the datatype: but there 
is no way in RDFS to express a 'closure' condition which expresses a 
limitation on the extent of a datatype class, since that in effect 
requires a universal quantification over the members of the class: so 
the (current) semantic requirement of identity on a class extension 
is an aberration in RDFS, expressing an effectively inexpressible 
condition. The above example is an entailment which seems to rely on 
implicit information (the cardinality of the boolean value space) and 
therefore appears as 'magical' in an RDFS rule set. This is why this 
identity condition prevented my stating a D-entailment lemma (and the 
above example involving booleans was the one that convinced me that 
to attempt to prove it was impractical). Herman correctly noted that 
the weaker semantics is more in line with the rest of the RDFS 
semantic framework, and overcomes this objection, allowing a full 
completeness result to be proved, which I feel is a valuable insight. 
Since the change required makes no difference to any previously noted 
entailment, I feel that it represents more of a correction to an old 
error than a real change; but my enthusiasm was curbed by the 
possibility that this change might have an adverse effect on OWL, 
hence my message to confirm that Herman's proposed fix to any such 
possible adverse effect is indeed adequate. I believe that it is.

>  > Jim and Guus, can this additional sentence be inserted into the OWL
>>  text so as to ensure compatibility? Note, this is not a change to the
>>  content or substance of OWL, only to the text so as to make it secure
>>  against a proposed editing of the RDF text. See end of this message
>>  for the proposed change to the OWL text in more detail.
>
>A proposed editing of the RDF text?  If there is some noticeable change to
>OWL from this proposed changed to RDF, I view the change as a substantive
>change to RDF during a period when RDF is not supposed to change.

There is no plan to change OWL. The effect of this modification is a 
slight weakening of the datatype semantic conditions, described 
above. We anticipate that OWL will require the stronger semantic 
conditions (since, unlike RDFS, OWL can indeed express and make use 
of class closure conditions); the situation is exactly similar to the 
stronger conditions required in OWL for subClass and subProperty. 
This requires that the stronger condition be stated explicitly in the 
OWL spec documents, if it is not already so stated.

>  > As you can appreciate, we need to move very quickly on this decision.
>>  I would be extremely grateful if you could give me a quick OK/not-OK
>>  on this so that the RDFWG can make a firm decision this Friday.
>
>I do not have sufficient information to determine whether this change is
>benign, and thus would vote against it, if I had a vote.
>
>>  Obviously any responsibility for any problems must be mine, but I
>>  would be grateful for your feedback. If you say not-OK then I will
>>  not make any of these changes, but I think that would be a pity as
>>  Herman has indeed identified a place where the RDF spec would be
>>  considerably better if his change were made. 
>
>Better in what way?  What are the consequences of this change?

The chief one is to bring the treatment of datatyped interpretations 
exactly into line with the way that class extensions are treated in 
RDFS, and thus to allow the statement and proof of a 'datatype 
entailment lemma' analogous to the RDFS entailment lemma (using a 
similar proof technique). I should have thought of this myself a long 
time ago, but I am glad that Herman spotted it in time to make it 
possible to achieve this degree of internal consistency in overall 
treatment. I think it will be generally useful to have RDFS engines 
available which have complete sets of inference rules for datatype 
entailment.

>This is literally our
>>  last possible chance to get this done. Thanks for your help.
>>
>>  Pat
>
>peter
>
>>  PS. A version of the RDF spec with this change made can be viewed at
>>
>>  http://www.ihmc.us/users/phayes/RDF_Semantics_2004.html
>>  particularly at
>  > http://www.ihmc.us/users/phayes/RDF_Semantics_2004.html#defDinterp
>
>This doesn't help very much without an indication of what the change is.

I thought my message made that clear, sorry.  The change can be 
viewed by comparing the above anchored text with the previous text at

http://www.w3.org/TR/2003/PR-rdf-mt-20031215/#defDinterp

The substantial changes are to the tables, but pieces of the 
subsequent 5 paragraphs have been also been rewritten to conform to 
the new table layout. (The only other change is to delete a remark on 
section 7.4 concerning the above xsd:boolean case, which no longer 
applies.)

Pat

-- 
---------------------------------------------------------------------
IHMC	(850)434 8903 or (650)494 3973   home
40 South Alcaniz St.	(850)202 4416   office
Pensacola			(850)202 4440   fax
FL 32501			(850)291 0667    cell
phayes@ihmc.us       http://www.ihmc.us/users/phayes