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Re: model theory for RDF/S

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Wed, 26 Sep 2001 13:26:05 -0400
To: phayes@ai.uwf.edu
Cc: www-rdf-logic@w3.org
Message-Id: <20010926132605J.pfps@research.bell-labs.com>
Good job. However,  I see several problems in the document.  Some of these
I view as significant. 

1/ The document does not sufficiently pin down the relationship between
   literal values and resources.  

   The model theory does not require that literal values and resources be
   disjoint.  Further, an RDF graph, as defined in Section 0.2, allows the
   head of edges to be labeled with literals.  This means that there is no
   significant difference between resources and literal values, nor between
   URIs and literals.

   The document, as it will probably be read, strongly suggests that
   literal values and resources are disjoint.  In Section 1.3, IEXT is a
   map into IR x (IR u LV), which will probably be read as requiring that
   LV and IR be disjoint.

   I think that the document needs to come down firmly on one side or the
   other.  Either it has to state that it is extending RDF to allow
   literals to be the subject of predicates, or it has to exclude the
   possibility of literals being the subject of predicates.

2/ The model theory does not assign meaning to RDF graphs.  Instead it
   assigns meaning to RDF graphs with an extra, nowhere-defined attribute
   on edges.  If this is supposed to be a model theory, then it should be
   rigorous, and not have any undefined junk floating around.

3/ The model theory maps literals into literal values and URIs into
   resources when it should be mapping nodes.

4/ The model theory breaks down for edges whose edge label does not map
   into a property as IEXT is only defined on properties.

5/ The model theory allows multiple URIs to map to the same resource.  I
   applaud this feature of the model theory, but it should be noted in the
   document outside of examples.

6/ The definitions of IEXT and IS should use the same notation.  

7/ The mapping of unlabeled nodes is to the ``domain'' of interpretations,
   but interpretations don't have domains.  Later on the mapping for
   unlabeled nodes is restricted to map to IR, which makes sense.

8/ In the model theory for RDFS, there is the requirement that all literals
   have rdf:type of LITERAL.  This now requires that literals be allowed in
   the subject position of predicates, which is forbidden in M&S and in the
   document as probably being read, but not forbidden in the model theory
   itself, although it has the effect of making all literals be resources.

9/ The model theory for RDFS is missing the requirement that the vocabulary
   contain all the RDFS ``pre-defined'' URIs.

10/ The model theory for RDFS is confusing with respect to the status of
    ICEXT.   ICEXT is not included in an interpretation, but appears
    prominently in the interpretation conditions.  Now it is not strictly
    necessary to have ICEXT be part of an RDFS interpretations, as implied
    in the document, but if so, then it would be much better to write the
    conditions without ICEXT (and also remove the condition that becomes
    vacuous).  

11/ The RDFS conditions are missing the fact that many ``pre-defined'' URIs
    belong to IC.

12/ The RDFS conditions are missing the range restriction on rdf:type.
    Without this restriction, ICEXT is not simply a convenience nor is
    rdfs:Resource an rdfs:Class in the model theory.  

13/ Many domain and range properties are missing from the RDFS
    interpretation conditions.  

14/ The RDFS schema-closure rule 1a has the effect of making all literal
    values be resources as all literal values have an rdf:type property
    because they are in the class extension of rdfs:Literal.  This is valid
    in the RDFS model theory, as all literals must be resources there, but
    is probably not expected.

15/ The RDFS schema-closure rule 1c also has the effect of making most
    literal values be resources.  This is a valid rule, because all
    literals are already resources, but is probably not expected.

16a/ Because of the missing domain and range properties the RDFS
    schema-closure rules 9a and 9b, are not valid.  The RDFS schema-closure
    rules are only valid because only properties have IEXT mappings.

16b/ Because of the missing range property on rdf:type, RDFS schema-closure
    rule 7 is invalid.

16c/ Because of the missing range property on rdf:type, all resources are
    subclasses of rdfs:Resource.

16.../  There are probably other consequences of the missing domain and
    range properties.

17/ Because of the complexity of RDFS, I won't believe the Schema Lemma
    until I see a completely worked out proof.

There is a typo in Figure 1.  It should say IEXT(1) instead of IEXT(I).

There is a typo in the RDFS conditions.  They should say
IEXT(I(rdfs:subPropertyOf)) instead of IEXT(rdfs:subPropertyOf).
Received on Wednesday, 26 September 2001 13:25:52 GMT

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