Re: RDF Semantics: two issues, connected to OWL

>Two issues need to be mentioned involving the RDF Semantics
>document, both connected to OWL, one smaller, one larger.
>(This adds to another issue, dealt with in [1], and not yet
>handled in the document: the central completeness claim
>does not hold, but could be made true by addition of one
>RDFS entailment rule.)
>Issue 1- It seems that two changes made to RDF Semantics
>during LC2 have not yet been incorporated completely
>in the definition of D-interpretations.

As already remarked in earlier messages: that I regard as a typo, and 
plan to get it changed before final publication , if the process will 
allow it.

>Issue 2- There remains a problem with the combination of the two
>documents  OWL S&AS (Semantics and Abstract Syntax)
>and  RDF Semantics, for which the optimal solution
>(in fact, any complete solution) seems to require changes to
>RDF Semantics [2].

You may well be right that the most elegant solution would be based 
on the technique you describe below. However, I do not agree that 
this is optimal, for a number of reasons. First, the fact that RDF 
reasoning  - even without datatyping - includes an accommodation to 
rdf:XMLLiteral  has been part of the RDF design for some time now, 
and the documents have drawn explicit attention to it.  The language 
was designed this way deliberately, as a result of WG decisions made 
partly in response to other comments; so to change this at this stage 
would be a major re-design.  Webont had adequate time to comment on 
this aspect of the design if they had wished to, and they did not. 
So if this fact causes some difficulty for Webont, then at this very 
late stage in the process I feel that it is up to Webont to correct 
the matter by making appropriate changes to the OWL documentation. 
However, read on.

>The problem I refer to in issue 2 is that the OWL design
>includes the possibility to do without the semantic conditions
>of XMLLiteral.
>This aspect of the OWL semantics design is not reflected in S&AS,
>and came to my attention only a few days ago [3] [4].

I am somewhat confused by this. You seem to be saying that the OWL 
documentation agrees with the RDF documentation, but that both of 
them are at odds with an undocumented (?) "OWL design". To my mind 
there is no problem here. The actual OWL design is that which is 
described in the documents. If someone misunderstands these documents 
then the appropriate course of action is for them to improve their 

>This possibility is not realized by S&AS because OWL is a
>semantic extension of RDFS, and each rdfs-interpretation
>satisfies the XMLLiteral conditions.

Quite. So this 'possibility' is in fact not a possibility.

I do not feel that any further action needs to be taken on your issue 2.


>I discuss a possibility to solve both issues.
>This possibility leads in addition, without much additional
>cost, to a possible, interesting extension of the RDF Semantics
>document, namely a sound and complete proof theory for reasoning
>with datatypes: an "RDFS-D-entailment lemma", generalizing
>the RDFS-entailment lemma to a large class of datatype maps.
>The two changes I refer to in issue 1 above are the omission of
>the terminology "from V" and the change not to require all
>possible literal values in LV.  In line 1 of the definition
>of D-interpretations the conclusion aaa in V would need
>to be added before I(aaa)=x, and line 2 of this definition
>could be generalized to include not all values in LV.
>The point of such a generalization would be - in line with
>the spirit of the document - that RDF aims at generality,
>so that semantic extensions have most freedom,
>and RDF is a flexible basis for the Semantic Web.
>(It was noted earlier that line 3 of this definition has also
>not been completely corrected, see [5].)
>The following definition of D-interpretations is formulated
>as a strict extension from the XMLLiteral conditions:
>Given a datatype map D and a vocabulary V, a D-interpretation
>of V is an rdfs-interpretation of V such that for all
><a,d> in D we have:
>- a in V and I(a) = d
>- I satisfies the triples
>     a type Datatype
>     a subClassOf Literal
>- if l=s^^a is a typed literal in V and s in L(d),
>   then IL(l)=L2V(d)(s) in LV  and  <IL(l),d> in IEXT(I(type))
>- if l=s^^a is a typed literal in V and s not in L(d),
>   then IL(l) not in LV  and  <IL(l),d> not in IEXT(I(type)
>This definition of D-interpretations would solve issue 1 above.
>If this change would be made, then the XMLLiteral conditions
>could be removed from Section 3 of RDF Semantics, and
>incorporated by including XMLLiteral in a datatype map.
>When the RDF Semantics document would be changed so that XMLLiteral is
>not necessarily present in every datatype map, then issue 2 would
>be solved as well, and the inconsistency between the documents
>OWL S&AS and RDF Semantics that was noted would be gone.
>If these changes would be made, then the RDF and RDFS entailment
>lemmas would need change as well, since they include XMLLiteral.
>Below I show that an attractive generalization of the
>RDFS entailment lemma could be obtained, extending the result
>to include a large class of datatype maps.
>Given a datatype map  D, consider the following "D-entailment rules":
>for each pair <a,d> in D, in order to replace rule rdf2:
>rule "rdf-a":
>   if E contains  uuu bbb lll, where lll = sss^^a is a well-typed literal,
>   then add  _:nnn type a, where _:nnn identifies a blank node
>   allocated to lll by rule lg.
>Define a "D-clash" to be a triple
>    b type Literal
>where b is a blank node allocated by rule lg to a literal s^^a, where
><a,d> is in the datatype map D for some d.
>The definitions suggested above lead to the following generalization
>of the RDFS entailment lemma:
>Suppose that S is a set of RDF graphs, G an RDF graph, and D
>a datatype map with disjoint value spaces and injective
>lexical-to-value mappings.
>Then S D-entails G iff there is a graph H that can be derived
>from S combined with axiomatic triples, by application of the
>literal generalization rule, rdf1, and RDFS and D-entailment
>rules, and that either simply entails G or contains a D-clash.
>The injectivity assumption can often be handled in practice with
>a suitable canonicalization operation.
>Assuming here the presence of rule rdfs14 :-) [1], this result
>holds: the details of the proof can be worked out.
>The assumptions on D are used in connection with the definition
>of the surrogate function sur.
>Herman ter Horst

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Received on Tuesday, 9 December 2003 12:00:43 UTC