The freedom to extend OpenMath and its utility

OpenMath is a standard for representing the semantics of mathematical objects. It differs from Presentation MathML in not being directly concerned with the presentation of the object, and from Content MathML2 in being extensible. How should these extensions be performed so as to maximize the utility (which includes presentation) of OpenMath? How could publishers have the freedom to extend and let consumers find their way with expressions discovered 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 OpenMath 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.