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Re: content mark-up: operators vs. relations?

From: Andreas Strotmann <strotman@nu.cs.fsu.edu>
Date: Thu, 28 Oct 1999 10:46:47 -0400 (EDT)
To: David Carlisle <davidc@nag.co.uk>
cc: devlinh@nwu.edu, www-math@w3.org
Message-ID: <Pine.GSO.4.10.9910281023380.27188-100000@xi.cs.fsu.edu>
> 
> The current best guess is that the restriction on not using <apply/>
> with `relation' elements will be dropped and so you will be able to
> uniformly use <apply/> (with reln being kept for largely historical
> reasons).
> 
> David
> 
I talked to someone (Stephen?) about this at one of the recent OpenMath
meetings, and I suggested using <reln> </reln> in the same way that the
<fn> </fn> is currently used (along with uniformly using apply).

Of course, this use would be less backward-compatible than what you
mentioned.  However, it would have some nice properties -- e.g., allowing
user-defined predicates to be marked up in such a way that the fact that
they are predicates (a very useful bit of semantics) is made explicit.  In
addition, this would allow user-specified quantifiers (e.g., the "almost
all" quantifier frequently used in functional analysis) to be used in a
consistent manner, namely in a combination of apply, reln, and bvar (a
similar use with fn instead of reln introduces operators, of course):

  <apply>                          <apply>
    <reln>                            <fn>
       almost all                        laplace transform
    </reln>                           </fn>

    <bvar>                            <bvar>
    ...                                 some var
    </bvar>                           </bvar>
    
    some expression                   some expression

  </apply>                         </apply>

Note that this pattern is very close to OpenMath's binding element.  It
does, however, go beyond OpenMath in introducing the concept of operator
types (that is, distinction between functions and relations).  [This
distinction was proposed for OpenMath in some of my early contributions,
but didn't make it into the specs.]

 -- Andreas


PS: I'm not sure at this point if the MathML on the right is currently
valid MathML.  If not, I hereby propose making it valid ;-)

PPS: This would also mean re-categorizing the boolean connectives and the
quantifier symbols as relations.
Received on Thursday, 28 October 1999 10:46:56 GMT

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