Re: semantics

I fully agree that new areas of mathematics are fluid and so it is
difficult to attach universally understood semantics to every
expression. For OpenMath this just means that "contexts" will
be locally developed and used until a particular community
decides that a field is mature enough to have contexts that
are in the official registry.

However two consenting programs must be able to share
semantic markup even if it is only locally understood. Thus
I might have a browser that works with a computational backend
and I still want all the good stuff like subexpression selection and
line breaking, but I do not want the semantics discarded by the
browser before it hands information to the backend. Even worse,
I do not want the backend to discard semantic information before
it gives it to the browser. This makes it difficult to carry on a high-level
discussion between the two apps if the backend has to continually
reanalysis information it originally gave the browser!

I think people sometimes overestimate just how much semantic
information is necessary. Whatever its commercial success, AXIOM
has at least proved that type information can go a long way in 
converting a general expression into a fully analyzed one. So stating
that a polynomial expression has a particular type of coefficients
will significantly aid those apps that can handle a bit of semantics.