Dear David, (01)
DL> We could gain benefits from defining good interfaces between
> notations which can represent some logic (such as OWL) and MathML.
> We could also think about how MathML takes advantage of ontologies. (02)
Many people become passionate about notations because any change
in notation can make their programs incompatible or obsolete. (03)
That is why Common Logic was defined with an abstract syntax,
examples of several different syntaxes, and the option for letting
anyone define whatever new syntaxes they might find useful. (04)
For CL, no notation has a privileged status, and any notation
that supports the standard semantics is as acceptable as any
other  provided that the notation has a formally defined
mapping to the abstract syntax. (05)
The Wolfram Mathematica system is an example of a very large
library of modules (called 'notebooks'), which support all the
major versions of mathematics. The Mathematica software uses
its own internal notation (which most users never see), and
it supports an openended variety of external notations:
a printed form for the traditional mathematical publications,
a simplified form for typed input, MathML, and a variety of
notations specialized for particular languages such as FORTRAN
or LISP. (06)
I would recommend an approach along the lines of Mathematica,
Common Logic, and many other systems that are based on an
abstract syntax but an openended number of concrete syntaxes. (07)
John Sowa (08)
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