[SCL] XML syntax options

[Pat Hayes]

>Murray,
>
>I think that we agree on what XML and MathML are,
>but we are using the word "semantics" differently.
>
>The excerpt you quoted says exactly what I said:
>MathML has no semantics -- i.e., it knows nothing
>about the meaning of any mathematical expression.
>The only thing it can do is specify the syntax:

Well, not exactly. MathML has 2 kinds of markup. The stuff I used was 
the 'content markup' and that indeed does have an (informally 
expressed, but adequate) intended semantics which corresponds 
reasonably well to SCL semantics. In particular it has all the 
logical connectives and the quantifiers, with their usual meanings 
specified. It uses a very generic 'apply' notion in what is I guess a 
standard approach to mathematical notation as consisting mostly of 
applications of operators to arguments, but that is quite consistent 
with a conventional logical semantics. It handles bound variables 
quite well.

One can argue that SCL ought to have markup which explicitly 
indicates the SCL basic syntactic categories, eg atoms versus terms 
and so on, so that there is no need for a parser to do this from 
context: after all, if you have to parse it, it hardly seems worth 
using XML in the first place. This is the only argument I can find to 
make against the use of MathML that seems convincing.

Murray (and Tanel, if Tanel is still with us): what is the purpose of 
using properties rather than child elements to indicate connectives 
and quantifiers? This seems arbitrary to me and somewhat unnatural, 
but I may be missing some significant XML advantage or subtlety.

>  > The intent of the content markup in Mathematical
>>  Markup Language is to provide an explicit encoding
>>  of the _underlying_mathematical_structure of an
>>  expression, rather than any particular rendering
>>  for the expression.
>
>Nota bene:  structure = syntax, not semantics.
>
>>  My point in this is that we *can* use MathML if our
>>  definitions of the things we'd use in MathML are
>>  defined identically, otherwise we can't...
>
>As I said before, they don't specify what any
>expression means -- i.e., the conditions for a
>statement to be true or false or the value of
>an expression, such as 2+2.

They don't give a model theory, but they give reasonably exact 
mathematical descriptions which I think are adequate to convey most 
of the intended content of SCL.  Substituting 4 for 2+2 is explictly 
given as one possible way to handle MathML content markup, by the 
way..

I guess my own feeling is that since MathML exists and is an accepted 
standard, and since it provides for almost all of SCL syntax, why not 
just use it? That is, I think we would need a positive reason NOT to 
use it if we decide not to: the onus is on any alternative proposal 
to explain what significant advantages accrue from using it rather 
than using an existing standard that seems adequate and has almost 
exactly the same motivation as SCL has.

Pat

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