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semantical annotations



Please allow me to attempt clarification on an issue I've
asked about, but I think hasn't been addressed specifically.

Bob has said that he feels that a means of hooking semantical
information to expressions would suffice for OpenMath's needs.  He
anticipates that simple type- and context-information are all that
would be necessary (perhaps for the near future), and that html-math
need only supply the hooks and not concern itself with the content of
the hooked information.

Bruce has discussed, at a high level, how annotations, macros, and
template-matching fit into the Wolfram Proposal.  My understanding of
his remarks is that the annotations are the means by which semantical
hooks may be attached to expressions.  Macros and template-matches
may do so by inserting annotations.

MINSE attaches semantical information via its `compound' mechanism.
(Ping also uses the term `macro' for a replacement mechanism within
MINSE, but the MINSE `compound' corresponds to the `macro' of the WP.
Is this a fair characterization?)  To retain some parallelism between
MINSE and the WP, I'll also call the semantical information attached
to a compound a `sematical annotation'.  (Let me know if this is a
harmful distortion.)

My question of several days ago regarded the need for more detailed,
notational information within a semantical annotation.  The level of
type-information which Bob mentioned in his message was that of a
simple text string (`sin' is semantically mapped to the sine function
from reals to reals of the basic Trigonometry context; or, if OpenMath
develops a notational scheme for such things this might come out as
`sin': sine\\Trigometry).  Type-information is itself dependent upon
understanding of a mathematical universe and is also dependent upon
objects mentioned locally within a mathematical argument.  Thus, it is
easy to imagine that one might want to attach local, notational
information to a type-specification.  The examples I gave before
involved vectors which might come from R^{n^2+n+1} or from another
object, which may not be `classical' and may be dependent upon local
parameters of the argument context, other than R.

Are we willing to say at this stage that our markup of mathematical
notation will *not* be part of the semantical annotations?  I believe
we have been saying that whatever markup is involved within the
semantical annotations is not markup which html-math should be
required to understand.


-Ron