OpenMath

OpenMath is the name of a markup language for specifying the meaning of mathematical formulae. Among other things, it can be used to complement MathML, a standard which mainly focuses on the presentation of formulae, with information about their semantic meaning. OpenMath can be encoded in XML or in a binary format.

OpenMath consists of the definition of "OpenMath Objects", which is an abstract datatype for describing the logical structure of a mathematical formula and the definition of "OpenMath Content Dictionaries", or collections of names for mathematical concepts. The names available from the latter type of collections are specifically intended for use in extending MathML, and conversely, a basic set of such "Content Dictionaries" has been designed to be compatible with the small set of mathematical concepts defined in Content MathML, the non-presentational subset of MathML.

OpenMath has been developed in a long series of workshops and (mostly European) research projects that began in 1993 and continues through today. The OpenMath 1.0 Standard was released in February 2000, and revised as OpenMath 1.1 in October 2002. Two years later, the OpenMath 2.0 Standard was released in June 2004. OpenMath 1 fixed the basic language architecture, while OpenMath2 brought better XML integration, structure sharing and liberalized the notion of OpenMath Content dictionaries.

The OpenMath Effort is governed by the OpenMath Society, based in Helsinki, Finland. The Society brings together tool builders, software suppliers, publishers and authors. Membership is by invitation of the Societies Executive Committee, which welcomes self-nominations of individuals who have worked on OpenMath-related issues in research or application. As of 2007, Michael Kohlhase is president of the OpenMath society. He succeeded Arjeh M. Cohen, who was the first president.

The well-known quadratic formula:

would be marked up like this in OpenMath (the representation is an expression tree made up from functional elements like OMA for function application or OMV for variables):

In the expression tree above symbols—i.e. elements like <OMS cd="arith1" name="times"/>—stand for mathematical functions that are applied to sibling expressions in an OMA which are interpreted as arguments. The OMS element is a generic extension element that means whatever is specified in the content dictionary referred to in the cd attribute (this document can be found at the URI specified in the innermost cdbase attribute dominating the respective OMS element. In the example above, all symbols come from the content dictionary for arithmetics (arith1, see below), except for the plusminus, which comes from a non-standard place, hence the cdbase attribute here.

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