OpenMath Content Dictionaries

Abstract

Content Dictionaries are structured documents used by the OpenMath standard [BCC⁺04] to codify knowledge about mathematical symbols and concepts used in the representation of mathematical formulae. They differ from the mathematical documents discussed in the last chapter in that they are less geared towards introduction of a particular domain, but act as a reference/glossary document for implementing and specifying mathematical software systems. Content Dictionaries are important for the OMDoc format, since the OMDoc architecture, and in particular the integration of OpenMath builds on the equivalence of OpenMath content dictionaries and OMDoc theories.

Concretely, we will look at the content dictionary arith1.ocd which defines the OpenMath symbols abs, divide, gcd, lcm, minus, plus, power, product, root, sum, times, unary_minus (see [OMC] for the original). We will discuss the transformation of the parts listed below into OMDoc and see from this process that the OpenMath content dictionary format is (isomorphic to) a subset of the OMDoc format. In fact, the OpenMath2 standard only presents the content dictionary format used here as one of many encodings and specifies abstract conditions on content dictionaries that the OMDoc encoding below also meets. Thus OMDoc is a valid content dictionary encoding.