From: Roger L. Costello <costello@mitre.org>

Date: Wed, 23 Jul 2003 12:02:29 -0400

Message-ID: <3F1EB195.239219F@mitre.org>

To: www-math@w3.org

Date: Wed, 23 Jul 2003 12:02:29 -0400

Message-ID: <3F1EB195.239219F@mitre.org>

To: www-math@w3.org

Hi Bill, Thanks a lot! The <approx/> element looks potentially useful as a way of expressing tolerance. In the example that you show: <approx definitionURL="http://www.openmath.org/cd/relation2#approx"/> <cn>-2</cn> <!-- the val is the exp of 10 --> What does this mean? Does it mean "All kilometer/mile pairs such that the value is within a tolerance of +/- 0.01? I believe that a tolerance (approx) value shouldn't be explicitly specified within the MathML. The reason is that for large kilometer/mile numbers 0.01 is a much smaller percent than for small kilometer/mile numbers, e.g, tolerance = 0.01 for kilometer=6300, mile=3914 is a much smaller percentage than tolerance = 0.01 for kilometer=0.25, mile=0.009 /Roger Bill Naylor wrote: > Hi Roger, > > Your e-mail raises an interesting point as regards to the tolerance > parameter to specify an "amount of slack" value for set membership. > There is an <approx/> element in the MathML spec. which one might hope > could be used for this purpose. However, that doesn't seem to give any > control over the accuracy of the approximation! There is an equivalent > OpenMath symbol in the cd relation1, but as it is only intended for > OpenMath/MathML alignment, that too doesn't give any accuracy. I have for > a while argued for an approx with accuracy and I guess that a relation2 > cd could be written which included such a symbol, then this cd may be > submitted to the OpenMath submission site: > > http://monet.nag.co.uk/cocoon/openmath/cdfiles/contrib/index.html > > This will put it in the submitted cd's. I think then that the intention is > that periodically the OpenMath organisation will review these cd's and > include the ones it agrees with as official (David (Carlisle) can you > correct me if I'm wrong). > > Given the cd's have been set up as above (an approx symbol in relation2, > where the first arg is the accuracy, 2nd and 3rd approx eq), the example > may be given as: > > <Class id="Distance"> > <equivalentInstances> > <!-- S = {k, m | k = m * 1.62} --> > <math> > <declare type="set"> > <ci>S<ci> > <set> > <bvar > definitionURL="http://www.openmath.org/cd/units_metric#kilometer"><ci>k</ci> > </bvar> > <bvar > definitionURL="http://www.openmath.org/cd/units_imperial#mile"><ci>m</ci> > </bvar> > <condition> > <apply> > <approx > definitionURL="http://www.openmath.org/cd/relation2#approx"/> > <cn>-2</cn> <!-- the val is the exp of 10 --> > <ci>k</ci> > <apply> > <times/> > <ci>m</ci> > <cn>1.62</cn> > </apply> > </apply> > </condition> > <list><ci>k</ci><ci>m</ci></list> > </set> > </declare> > </math> > </equivalentInstances> > </Class> > > I think that will do what you want? > > If things have not been set up as required in an OpenMath CD, it is > sometimes possible to use the MathML semantics element to specify the > required semantics. The syntax of this element is described in the MathML > spec: > http://www.w3.org/TR/MathML2/chapter4.html#N36079 > > I hope this helps, > > BillReceived on Wednesday, 23 July 2003 12:02:32 GMT

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