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Re: Semantic information for math representations of physics

From: <RobertM@dessci.com>
Date: Fri, 28 Jan 2005 10:38:48 -0600
Message-Id: <200501281638.j0SGcm023162@intuition.geomtech.com>
To: joebmath@yahoo.com
CC: www-math@w3.org


Hi.

My initial reaction is that questions like yours require a context.
MathML provides a number of syntactic hooks in content MathML for
extending the language.  Thus it is fairly easy to devise a scheme for
representing Dirac operators, densities, sets, categories and so on in
content MathML.  The standard thing to do would be to use the
definitionURL attribute to label <ci>'s or <csymbol>'s according to
some externally defined scheme.  Similarly, the <declare> element and
various logic constructs could be pressed into service to identify
various relationships between objects defined in this way.

The main question, though, is what you want to accomplish by doing
so.  If plan to use your markup yourself, or within a group or project
that can all agree to use a set of conventions, then you are fairly
free to make up anything that serves your needs.  However, if you need
something that will be interoperable between various projects and
software applications, you have a much bigger challenge.  There are
various groups using content MathML that have extended it in various
ways to meet their needs, but I sort of doubt that you will find
someone who has a scheme all set up that you can just use.  For
example, there is a Conexions project at Rice University using content
MathML for electrical engineering (among other things).  They might
have defined something for a Dirac operator, but I'm guessing they
don't have a PhysicalObject.

Similarly, the most extensive and institutionally stable set of
semantic extensions to content MathML comes from the OpenMath project.
They have a system for defining, reviewing, publishing and maintaining
"content dictionaries" that can provide the labels for definitionURLs.
A number of research projects and software applications like theorem
provers are set up to work with OpenMath.  So if you are looking to
set up a very broadly useful set of extension for physics, creating
and promoting OpenMath content dictionaries for your stuff would be a
good way to go.  But now you are talking about a major, long-term
project.

Hope this gives you an idea of your range of options.  If you want to
fill in the context some, I'm sure folks will be happy to get into the
details more.

--Robert


> I am interested in representing equations in physics
> using content MathML. This is something I'm new to, so
> I'm exploring the ability of MathML to help me.
> 
> One deficit in the math concepts I have found so far
> is that the Dirac Delta Function is not represented.
> Is this correct?
> 
> I am aware of the recommendation regarding physical
> units. This does not, however, cover the full semantic
> information that representing an equation in physics
> requires. Here are some other requirements:
> 
> (1) A key requirement is to represent, for example,
> that /rho represents the density of a certain physical
> object.
> 
> (2) I might also want to give names to certain
> constructs, such as NewtonianSpaceTime for the
> specific instance of a metric-space (and time) of
> Newtonian physics, or the name of Newtons2ndLaw to a
> statement about F=ma.
> 
> (3) Vectors are often elements of NewtonianSpaceTime.
> Can I declare them to be of that type? I would also
> like to declare PhysicalObject as a class. Can I do
> this?
> 
> Any insights are welcome.
> 
> Regards,
> Joe C. 

------------------------------------------------------------------
Dr. Robert Miner                                RobertM@dessci.com
W3C Math Interest Group Co-Chair                      651-223-2883
Design Science, Inc.   "How Science Communicates"   www.dessci.com
------------------------------------------------------------------
Received on Friday, 28 January 2005 16:39:23 GMT

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