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Re: model theory for RDF/S

From: Pat Hayes <phayes@ai.uwf.edu>
Date: Thu, 27 Sep 2001 12:48:54 -0500
Message-Id: <p05101044b7d90f8327da@[205.160.76.184]>
To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
Cc: www-rdf-logic@w3.org
>form From: Pat Hayes <phayes@ai.uwf.edu>
>Subject: Re: model theory for RDF/S
>Date: Wed, 26 Sep 2001 17:23:45 -0500
>
>>  >One more problem with the model theory.
>>  >
>>  >Even if all aspects of reification and containers are removed from RDF>
>>  >There is still the matter of rdf:type
>>  >
>>  >In ``5. Formal Model for RDF'' of M&S, there are the requirements that
>>  >
>>  >  5. There is an element of <I>Properties</I> known as RDF:type.
>>  >
>>  >  6. Members of <I>Statements</I> of the form {RDF:type, sub, obj} must
>>  >     satisfy the following: sub and obj are members of <I>Resources.</I>
>>  >     [...]
>>  >
>>  >These conditions are not captured in the model theory.
>>
>>  Well, they are in a sense.  I am not sure how to interpret 5 as a
>>  requirement on RDF, other than as a syntactic requirement on the
>>  vocabulary, in which role it has no bearing on the model theory of
>>  RDF.
>
>Yes, 5. is a requirement on the vocabulary, namely that it contains at
>least this element.  This in turn may have effects on the model theory,
>such as having effects on the cardinality of IP in any interpretation that
>is a model of an RDF graph.  This, in turn, may have consequences, such as
>the (silly) theorem that all models of RDF graphs have at least one
>property.

Ah, point taken. Indeed it does require that IP be non-empty. I will 
put a remark in about that, thanks.

>
>>  Like the rest of the M&S, condition 6 is careless about use and
>>  mention; I assume it was intended to say that the subject and object
>>  *denote* members of the set of Resources. (This is a semantic
>>  requirement in the metatheory, not an assertion in RDFS, since it
>>  uses the form:  <I>Resources.</I> rather than:
>>  <code>rdfs:Resource</code>, right?)  With this understanding, it
>>  seems to follow automatically, since IR is required to consist of
>>  resources by the model theory.  On the other hand, if it intended to
>>  be interpreted strictly literally, then it seems to be an assertion
>>  about the semantic status of pieces of RDF syntax, which would have
>>  no model-theoretic consequences at all in the absence of reification.
>
>6. has the implication that ``classes'' have to be resources (i.e., not
>literals that are not resources).  This is not captured in the RDF section
>of the model theory document.

Seems to me that these conditions only have any effect on the formal 
language in RDFS, since RDF has no way to refer to classes as such, 
including the class of properties.  RDF properties - ie arc labels in 
an RDF graph - are required (by the RDF syntax) to be URIs which are 
required (by the model theory) to denote resources (members of IR), 
but I don't see any other consequences of this for the meanings of 
any expressions in the actual formal language until we get to RDFS.

Pat

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Received on Thursday, 27 September 2001 13:48:45 GMT

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