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Re: Semantic information for math representations of physics

From: John Fletcher <J.P.Fletcher@aston.ac.uk>
Date: Thu, 03 Feb 2005 13:06:46 -0000
To: Paul Libbrecht <paul@activemath.org>
CC: www-math@w3.org
Message-ID: <420221E6.22244.C670B4@localhost>

I would like to join in this discussion as a potential user, at the stage 
of knowing what I want to do and having some design choices.

I have computer programs which can compute algebraic 
expressions. I want to compute, output and store results.  It would 
be good also to attach metadata e.g. data, time, purpose to the 
computation.

I idenitified content MathML as providing the basic coding, except 
that I need to go beyond that, as I am working in Clifford Algebra, 
so I need to extend MathML.

I could extend it in an arbitrary way, or use RDF to define a set of 
extensions.  

As an example of what I am doing

x{1} + y{2}     is the vector (1,2)

1 + {1,2}       is the sum of a scalar and a bivector.

I need the capability to represent terms {i,j,k....} in a simlar way to a 
complex number or a quaternion.

I can provide more information

John Fletcher


is m

Copies to:      	RobertM@dessci.com, www-math@w3.org
From:           	Paul Libbrecht <paul@activemath.org>
Date sent:      	Thu, 3 Feb 2005 13:51:16 +0100
To:             	JB Collins <joebmath@yahoo.com>
Subject:        	Re: Semantic information for math representations of physics
Forwarded by:   	www-math@w3.org
Date forwarded: 	Thu, 03 Feb 2005 12:51:55 +0000

> 
> 
> Le 3 févr. 05, à 13:20, JB Collins a écrit :
> 
> > [...] Those things being said, I am going to take your
> > response as guidance that says something like "when
> > concepts are defined in MathML, use them; when they
> > are not, for user extensibility, rely on OpenMath."
> 
> What we know:
> - OpenMath and MathML are informally compatible (that is, everyone
> believes so) - the policy in the two bodies (W3C Math Working/Interest
> Groups and the OpenMath society) converge (which was not the case at
> the time MathML content was created, I think).
> 
> MathML-content has been started with a view that an element-name is
> the best representation for a mathematical symbol... thus it needs to
> declare all these element-names, for example, in the DTD, hence
> specify them all part of the language specification. Extensibility is
> not normalized
> 
> OpenMath has started with extensibility in mind from the start on.
> There is no element in the OpenMath language  that denotes a precise
> mathematical "notion", "symbol", "concept". All of them are described
> in content-dictionaries the management of which is somewhat easier.
> Content-dictionaries can be contributed and modified easier than a
> language specification.
> 
> There has been some discussions, probably not enough, about bringing
> MathML and OpenMath in sync but this has not been finalized.
> 
> There are intents to promote a tighter compatibility declaration such
> as cross-pointing between OpenMath symbols and MathML symbols and
> indicating best practice for the usage of OpenMath along with MathML.
> 
> Comments and suggestions about this would be most welcome!
> 
> Both OpenMath and MathML, however, do not treat the problematic of
> grounding the extension of a symbol, for example, using a definition.
> That definition could be formal or informal, it would, typically, need
> further developments such as theorems, proofs, or axioms. This last
> step, an attempt at complete representation of mathematical documents
> is the goal of the OMDoc language, http://www.mathweb.org/omdoc/.
> OMDoc's user-base or gang of tools is not as rich...
> 
> Physics has not been touched much in OMDoc, as far as I know. I would
> view such statements as the formal statement about the nature of an
> observable as being a possible extension of OMDoc. (which could even
> be something like the statement of the type of a symbol).
> 
> OMDoc theories are not, yet, convertible back into an OpenMath content
> dictionary. This is a known issue which we intend to tackle in the
> ActiveMath authoring gang of tools (headed by jEditOQMath,
> http://www.activemath.org/projects/jEditOQMath).
> 
> OMDoc documents are the base of our ActiveMath learning environment.
> The formal part of OMDocs are not much used yet though there are some
> intents in the direction of proof-planning usage for education...
> 
> The content in the Mizar Mathematical Library is one of the most
> famous formal mathematics libraries and, clearly, conversion from
> there to OMDoc is something that interests many involved in OMdoc and
> a start of it has been attempted by Michael Kohlhase (on this list
> usually) among others. I heard of no results thus far.
> 
> I did not know of the goal of Mizar encoding to provide a platform for
> the exchange of mathematical documents between theorem provers... the
> conversion of the logical foundation is, as far as I know, often a
> very tough problem when considering such exchange and the logical
> foundation of Mizar documents is very high level, I heard.
> 
> paul
> 
> > As an additional question to throw in, I am also
> > interested in knowing if MathML / OpenMath borrow or
> > cooperate with the MIZAR project. While I started this
> > thread on the MathML reflector, you pointed to
> > OpenMath and its use for interchanging documents for
> > theorem provers. The MIZAR project provides a similar
> > capability. While they seem primarily focused on
> > supporting mathematicians, there seems to be a lot to
> > borrow from.
> 
> 
> 

-------------------------------------------------------------------
Dr John P. Fletcher          Tel: (44) 121 204 3389 (direct line)
Chemical Engineering and Applied Chemistry (CEAC),
School of Engineering and Applied Science (SEAS),
Aston University,            Fax: (44) 121 359 4094
Aston Triangle,              Email: J.P.Fletcher@aston.ac.uk
BIRMINGHAM B4 7ET  U.K.      CEAC Web site 
http://www.ceac.aston.ac.uk/
Received on Thursday, 3 February 2005 13:04:13 GMT

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