> QUESTIONS
> 
> 1. How does this aspect (information ~ uncertainty) of Shannon's work relate
> to data exchange using XML? 

That is a rather broad question, like "how does Newton's work relate
to the construction industry?"   My guess is that XML is somewhat
against the grain of Shannon's thought (without contradicting it) :
The point of markup is to add redundancy so as to increase the
probability of information surviving noisy channels or the passage of
time that tend to degrade  shared assumptions about the inherent
structure of messages.  Binary data is pretty meaningless without
knowing the way the bits are broken up into fields, the byte-order of
the integers, etc. XML is more akin to natural language with its
redundancy, irrelevancies, etc., which Shannon was trying to factor
out.

> 
> 2. A schema is used to restrict the allowable forms that an instance
> document may take.  So doesn't a schema reduce information?

Right, that's the whole point.  This is most easily seen in
schema-based data compression along the lines of ASN.1 -- If you
constrain the diversity of information that could be exchanged, then
it takes fewer bits on the wire to convey something meaningful.   More
generally, schemas reduce the set of possible markup and values within
the markup, so they reduce the expressiveness of one authoring
according to the schema. The value offered in return is that the
shared assumptions about inherent structures of messages make it
easier for stupid machines to "validate" the messages, for simple
programs to make effective use of the messages, etc.