Re: quantifiers

Hi Robert,

> > - What is the reason for not including the two standard <quant>ifiers,
>    <forall/> and <exists/>?
> 
>    I think we will not be including <forall/> and <exists/> because
>    of exactly what started to happen to you, in your comment; this
>    addition starts to propagate changes like crazy.  

I hate to say this, but isn't that a sign that there is a real problem
with the current MathML design lurking here?  After all, additions
ideally should NOT "propagate changes like crazy" -- in fact, they
shouldn't propagate any changes at all, only additions.  And MathML
should be open to additions, no?

Also, doesn't it strike you as odd that you're about to exclude the
fairly well-behaved and easy-to-markup standard variable-binding
quantifiers while at the same time including the much more problematic
and difficult-to-markup variable-binding operators?  And isn't it true
that the content mark-up for the latter is affected almost exclusively
when introducing the former?  And again, shouldn't that be read as a
sign that the changes introduced by adding the standard quantifiers are
necessary ones for "good" content markup?

> However, it is
>    still being discussed, and if someone can really make the case
>    that the addition won't introduce some serious logical
>    inconsistency, we may still do it.

Personally, I'd be much more happy if MathML 1.0 would *include* simple
quantifiers and *exclude* generalized quantifiers (including operators
like int, sum, limit) than vice versa.   Such a MathML content markup
would have a much greater chance of being extensible "without
introducing some serious logical inconsistency" than the current design
does, I suspect.  The reason for this suspicion is that such a MathML
1.0 would correspond fairly closely to the structure of entry-level
symbolic logic formulas, and these have been studied for such a long
time and so intensively that a software engineer may reasonably assume
them "safe".  Generalized quantifiers (including operators) are
"advanced" problems by comparison, and may not be as well understood
yet, thus requiring further study before attempting to define "logically
consistent" content markup for them.


Best,               Andreas

Received on Friday, 30 January 1998 17:42:48 UTC