# The Freedom to Extend OpenMath and its Utility

## Abstract:

OpenMath [6] is a standard for representing the semantics of mathe-
matical ob jects. It differs from Presentation MathML [8] in not being directly
concerned with the presentation of the ob ject, and from Content MathML
2 [8] in being extensible.
How should these extensions be performed so as to maximise the utility
(which includes presentation) of OpenMath? How could publishers have the
freedom to extend and let consumers find their way with expressions disco-
vered on the Web? The answer up to now has been, too often, to say “this
is not specified” whereas the existing content dictionary mechanism of Open-
Math allows it to include formal properties which state mathematical facts
that should stay uncontradicted while manipulating the symbols.
The contribution of this paper is to propose methods to exploit the
content dictionaries so as to allow an OpenMath-consuming tool to process
expressions even if containing symbols it did not know about before. This
approach is generalized to allow such newly discovered symbol to be, for
example, rendered or input.

## Published:

Journal of Mathematics and Computer Science, number 59, Special Issue on Mathematical Knowledge Management, Manfred Kerber (ed).,
2008, Birkhäuser Verlag.