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RE: Goals verses syntax in MathML
[Stan Devitt]
> From Andy Felt:
>
> Here are my questions:
>
> 1) Are we really trying to come up with a standard way to
> code *and display* all common mathematical expressions, such
> as the differential operator? This seems like an admirable
> but impossible task. If you ask 10 mathematicians how to
> display the differential operator, you will get 5 different
> answers. So, for automated search-ability, are we giving up
> quite a bit of display flexibility?
>
Precisely the point. This is why there is no attempt in
MathML 1.0 to dictate either appearance or semantics.
The view taken is that the author is in full control.
If an author wants to specify how his/her differential
operator is to appear, they do so, using the MathML 1.0
presentation tags.
If they are more concerned about communicating
the meanings of their formulae than the appearance,
they use content tags, perhaps overriding the default
definition to use their own variant.
If they want to control both, they specify both
a presentation and the semantics, grouping them
using the <semantics> tag.
The role of MathML is to facilitate communication.
The author can say as little or as much about their
math objects as they like.
It would be a serious mistake to adopt a design
that actively prevented the recording of either
kind of information.
> 2) If there are translators from LaTeX to MathML, how can
> this `context' possibly be included? LaTeX did not meet the
> needs of MathML because it is only display oriented (i.e.
> the same expression may stand for two different ideas,
> depending on context), but how can a translator add such
> context?
>
Inferring semantics when the author neglected to
record it in the first place is a hard task.
A naive translator should probably just build
a "presentation", ignoring the semantics entirely.
On the rare occasions when the document has been
encoded with semantics in mind, perhaps by using
special macros to record the semantic expression
tree rather than the presentation, you can do better.
There has been some work done on heuristics to guess at
meaning, but it is always only a guess.
This problem is completely outside the scope of MathML.
> 3) Why is automated searching for math syntax so important?
> If I am searching for a paper on trigonometry, I would
> search for `trigonometry', not \cos (or the MathML
> equivalent). Or is it searching within a document that we
> are talking about?
>
> Again, I appologize if I am rehashing old material. For
> what my vote is worth, I would rather stick to a
> display-only language, tell the browser developers to
> include a LaTeX compiler, and be done with it. However, I
> can understand that searching for context-based material
> might be important to some people.
>
Consider the analogous problem of searching a collection
of tex documents for papers involving arrays.
A search for a TeX or LaTeX array construct is
unlikely to be much use. The structures get used
frequently in the document markup for their visual
properties rather than their mathematical properties.
"If" a document were marked up using semantic tagging,
then it would be possible to search for mathematical
arrays.
So the types of questions that you might ask are
Find all paper or formulae involving:
1. Integrals of of a product
2. matrices of trig functions
3. quotients
4. uses of the product defined in the 1888 paper of ...
Stan Devitt, Ph.D.
Senior Math Developer
Waterloo Maple Inc.