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semantical annotations

To: w3cmatherb@w3.org

Subject: semantical annotations

From: Ron Whitney <RFW@MATH.AMS.ORG>

Date: Sat, 07 Sep 1996 10:46:01 0400 (EDT)

From w3cmatherbrequest@www10.w3.org Sat Sep 7 10: 46:37 1996

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Messageid: <842107561.847733.RFW@MATH.AMS.ORG>
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 contextinformation are all that
would be necessary (perhaps for the near future), and that htmlmath
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
templatematching 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 templatematches
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
typeinformation 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). Typeinformation 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 typespecification. 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 htmlmath should be
required to understand.
Ron