Unifying Math Ontologies: A Tale of Two Standards

One of the fundamental and seemingly simple aims of mathematical knowledge management (MKM) is to develop and standardize formats that allow to “represent the meaning of the objects of mathematics”. The open formats OpenMath and MathML address this, but differ subtly in syntax, rigor, and structural viewpoints (notably over calculus). To avoid fragmentation and smooth out interoperability obstacles, effort is under way to align them into a joint format OpenMath/MathML 3. We illustrate the issues that come up in such an alignment by looking at three main areas: bound variables and conditions, calculus (which relates to the previous) and “lifted” n-ary operators. Whenever anyone says “you know what I mean”, you can be pretty sure that he does not know what he means, for if he did, he would tell you. — H. Davenport (1907–1969)