[Om3] Being pragmatic about the semantics of, eg, variables and functions

[Professor James Davenport]

On Tue, March 24, 2009 10:04 pm, David Carlisle wrote:
>
>> That's not quite the same thing (fortunately). If Chapter 4 is merely A
>> translation Prag->S (which is what I would hope) then evolving OM will
>> let
>> us improve a "best efforts" translation, which would be a nice position
>> to be in.
>
> it's not just _a_ translation. In MathML 1 and 2 the meaning of the
> content markup was given in a CD-like appendix using a notation and
> prose style that was unique to mathml. Under that model, there is scope
> for any number of "best effort" conversions from MML to OM.
>
> In MathML3 the meaning of the content markup is defined by its
> translation to strict. So (unless there is an error in the spec, which
> happens of course) an alternative, later, translation to strict mathml
> must produce something that is mathematically equivalent, as the element
> is defined by the specified translation.
Understood, and apologies if that wasn't clear. But there might be
pragmatic markup whose meaning wasn't defined, or where we can think,
maybe as CDs evolve, of "better", but still mathematically equivalent, OM.
>> Which essentially means, as I understand it, that 'condition' is either
>> IN or OUT, irrespective of CDs.
I meant, "in strict", sorry.
> yes but of course it doesn't have to mean anything. You can construct
> all kinds of expressions that don't have any obvious semantic
>
> <apply><cn>1</cn><condition><pi/></condition><cn>2</cn></apply>
>
> is valid mathml which perhaps means the function 1 applied to 2,
But as I understand it, the P->S would fail to convert this. Am I wrong
here? This is a key illustration.
[I'll come back to the rest later]

James Davenport
Visiting Full Professor, University of Waterloo
Otherwise:
Hebron & Medlock Professor of Information Technology and
Chairman, Powerful Computing WP, University of Bath
OpenMath Content Dictionary Editor and Programme Chair, OpenMath 2009
IMU Committee on Electronic Information and Communication