Re: RDF Model Theory Working Draft: Comment

Greetings. You wrote (in reply to Graham Klyne):
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The words "node"
and "arc" are not used at all in the formal definition of I, the
interpretation.  What is unclear in the draft, however, is the
provenance of the 'E' in I(E) - the denotation rules canvass literals,
urirefs *and*, lo and behold, triples analysed in terms of all three
parts [cf the alternative graph I outlined.] Nowhere is it said (and
nowhere does it seem necessary to say) that each element in IEXT "is"
or "maps" to an "arc", let alone a single one.
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Your first statement is correct. As I mentioned in my last message, 
interpretations are defined on a vocabulary, not on a graph or a 
document. Any such interpretation does however *determine* the 
meaning (in that interpretation) of any RDF graph, according to the 
semantic rules given in the MT document; and those rules do mention 
nodes and arcs.

This style of definition is considered normal good practice in 
defining a model theory; the rules that extend an interpretation of a 
simple vocabulary to provide meanings for any expression of the 
language are often called the truth-conditions (or truth-recursions 
to emphasize that they have to be stated in such as away as to track 
any recursive constructions in the syntax; there are no such 
recursions needed for RDF, however.) The standard style for stating 
truth-conditions is to give, for each syntactic construction in the 
grammar, rules which specify the interpretation of an expression of 
that syntactic class in terms of the interpretations of its immediate 
subexpressions. Since names or identifiers are usually the atomic 
cases in any syntactic specification, the natural way to define an 
interpretation is to assign appropriate structures to the names and 
then work up to larger structures, following the syntactic 
specification. The RDF model theory starts with labels, moves to 
labelled nodes (trivial), then to ground triples or directed edges, 
then to ground graphs, then to arbitrary graphs.  Perhaps I should 
have explained all this more carefully; it is difficult to strike a 
balance between writing a tutorial and a reference document.

I am not entirely sure what you mean by the "provenance of the 'E' in 
I(E)"; E here is a variable used in the document itself to indicate 
any well-formed 'piece' of RDF which is assigned a value in an 
interpretation. ("Piece" here is meant to exclude, for example, any 
parts of complex URIs, or the innards of literals, if they have any; 
but to include nodes, arcs, triples (node-arc-node subgraphs) and 
graphs (equivalent to sets of triples).) Each case is stated (I hope) 
reasonably clearly, along the lines "If E is a node then...". If you 
find any ambiguities please let me know.

Elements of IEXT do not map either from or to arcs. Extensions are 
relations on elements of the semantic domain IR, not on the graph 
syntax.

I hope this helps.

Pat Hayes

PS: It seems clear from your messages that, having misunderstood the 
intended notion of RDF graph, you are working with a different 
notion.  Much of the model theory and indeed the entire RDF document 
corpus will be incomprehensible if read in your way, however, so I 
would urge you to re-think things more long the lines suggested in 
the RDF M&S, in spite of the technical error that you have indeed 
noted in the text.

You also wrote:
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I'm sorry, but this smacks of factitious retrofitting.
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Yes, that is a very elegant restatement of the charter of the RDF 
Core WG, to factitiously retrofit the RDF spec.
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