Patrick,
I am using netscape composer to create some HTML, but I will leave it to you to merge with your document. (I am not sure what editor you are using, I believe Composer creates fairly simply HTML that should be straight forward to merge).

I suggest the following edits to your document, my text is not yet ready, but an early version is below.
 

  1. In the introduction

    2. The TDL scheme, also known as "PDU" or "PD", is a fusion of the idioms from two earlier schemes "P" and "D" (or "DAML") along with the conceptual model from "U" (omitting the URV based idiom).  When type information is omitted the Model Theory for TDL captures the ambiguous typing of the Perl programming idiom (PL).
  2. Delete text (the same content will be addressed with new section). I find this is too aggressive because it is so early in the document.

    3. It should be noted up front that the TDL datatyping scheme

    does not require modification to the present RDF graph model
    does not require modification to the present RDF/XML serialization
    does not require modification to the present N3 notation
    does not require modification to the present NTriples notation
    reflects common RDF usage, adopting popular idioms already in use
    reflects common XML Schema usage for the typing of literals
    provides for both global (implicit) and local (explicit) typing concurrent ly

  3. Modify text on TDL & Model Theory

    4. OLD:
    In accordance with [RDF MT], the primary RDF syntax used in the TDL scheme is based on tidy graphs (a tidy graph is the one in which no two nodes carry the same label). The interpretation of each literal is assumed fixed and determined by its content. (For example, the interpretation of literals could be defined as an identity mapping.) NEW:
    The formal treatment of TDL is presented as a modification to the RDF Model Theory. Datatyping is achieved during interpretation. Each occurrence of a literal Unicode string may have its own node in the graph and is interpreted according to the map(s) associated with the datatype(s) associated by TDL with that node. The graph may be ill-formed because of datatyping problems (e.g. "three" is not an integer). The informal intent of TDL is to capture the normal programming paradigm that the input syntax uses the lexical space of datatypes, and the "meaning" is in the value space of the datatype. However, for technical reasons (mainly that the typing in RDF MT is part of the model rather than the interpretation), the interpretation of each Unicode string node in the graph is given as a lexical-value pair within the Universe, which most of the time is treated as being the value component. As always, the intent of the Model Theory is to capture concepts such as entailement, consistency etc. but not to indicate an approach to implementation. In particular, the existence of lexical-value pairs within the Universe of Interpretation is not intended to indicate a deep metaphysical belief in such things!
  4. Delete appendices A&B. This stuff is not needed for TDL and acts as possible obstacles to other members of the group from supporting TDL. I suggest that if TDL is accepted then these appendices could form a Techinal Note or something like that. (Also I have appendices to add).
  5. Add my section "Introduction to the Model-Theoretic Interpretation" at section 2.2
  6. Add new section comparing TDL with the requirements (this replaces the deleted text from the intro).
  7. Add my appendix "The Model Theoretic Interpretation" at end.
  8. Add my appendix "XML Schema Union Datatypes in RDF" at end.
  9. I wonder whether in 3.3 we should have more text explaining why TDL has full compatibiility and S does not. (e.g. "In TDL the local and global typing mechanism are the same: in the model theory the representation is identical, the lexical-value pair. This can be contrasted with S where the global idom (idiom B) operates entirely within the lexical space and cannot freely interoperate with the local idiom (idiom A) which operates principally in the value space. In S, idiom A, this allows different lexicalizations of the same value space (e.g. octal and decimal integers) to interoperate, whereas in TDL such interoperability is not possible. S, idiom B, does not prohibit such interoperability, but is highly problematic.")
  10. Can we change the Model Theory reference to be a more recent version e.g. http://lists.w3.org/Archives/Public/www-archive/2002Jan/att-0007/01-RDF_Model_Theory.htm

 

An Introduction to the Model Theory for TDL

TDL is formalized as changes to the existing RDF Model Theory.
Datatypes are viewed as in Patel-Schneider's work [OWL: URL:???]. That is each datatype has four components, a URI, a lexical space, a value space, and a mapping. Unlike previous work, the mapping is a relationship rather than a function. This is specifically to accomodate XML Schema Union datatypes. For all other datatypes the mapping is a function. Each datatype is a resource and is found in the Universe of interpretation.
An RDF interpretation is with respect to some set of datatypes, minimally containing xsd:string, which can be viewed as the default datatype.

Terminology

We modify the terminology of the Model Theory to differentiate between literals before datatyping and literals after datatyping. The modification is:

The Interpretation of Unicode Nodes

Each Unicode node is interpreted as a literal-value pair. The literal-value pair must occur in the map of some datatype. (Hence the requirement that xsd:string is in the set of datatypes, this ensures that there is at least one possible interpretation of every Unicode node). The unicode string component of the literal-value pair is the label of the Unicode node. If there is no type information available for a Unicode node, it can hence be interpreted according to any of the supported datatypes, as long as the Unicode string is in the literal space of the datatype. In this way, TDL formalises the PL proposal.

The Universe of an Interpretation

The Universe is formed by the union of: i.e. The Universe contains resources, typed data values, and literal-value pairs.

The Interpretation of Datatype URIs

The interpretation mapping IS is restricted to mapping any datatype URI in V to the corresponding datatype in IR. That is, a datatype URI does identify a datatype.

The Interpretation of Asserted Triples

Asserted triples are interpreted with respect to the function IEXT. However, the range of IEXT is extended to permit any pair of objects from the Universe.
IEXT is then restricted to respect rdf:value as equality and encodes the supported datatypes.

i.e. IEXT(rdf:value) is the identity on the universe.
For if d is a datatype then,
    IEXT(rdf:type) contains the pair ( (unicode-string, value), d )
    if and only if (unicode-string, value) is in the map associated with d.

IEXT is also required to be neutral with respect to the lexical space on all other properties.
i.e.
   if (u1,v) and (u2,v) are two literal-value pairs in the universe and r1, r2 resources in IR then

   ( r1, (u1,v) ) is in IEXT(r2) iff  (r1, (u2, v) ) is in IEXT(r2)

BUG