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>

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 UTC

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