OMDoc (Open Mathematical Documents) is a

semantic Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and comput ...

markup format for

mathematical Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

documents. While

MathML Mathematical Markup Language (MathML) is a mathematical markup language, an application of XML for describing mathematical notations and capturing both its structure and content. It aims at integrating mathematical formulae into World Wide Web ...

only covers mathematical formulae and the related

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 s ...

standard only supports formulae and “content dictionaries” containing definitions of the symbols used in formulae, OMDoc covers the whole range of written mathematics.

Coverage

OMDoc allows for mathematical expressions on three levels: ;Object level:Formulae, written in Content

(the non-presentational subset of MathML),

or languages for

mathematical logic Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of for ...

. ;Statement level:Definitions, theorems, proofs, examples and the relations between them (e.g. “this proof proves that theorem”). ;Theory level:A theory is a set of contextually related statements. Theories may import each other, thereby forming a

graph Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discre ...

. Seen as collections of symbol definitions, OMDoc theories are compatible to OpenMath content dictionaries. On each level, formal syntax and informal natural language can be used, depending on the application.

Semantics and Presentation

OMDoc is a semantic markup language that allows writing down the ''meaning'' of texts about mathematics. In contrast to

LaTeX Latex is an emulsion (stable dispersion) of polymer microparticles in water. Latexes are found in nature, but synthetic latexes are common as well. In nature, latex is found as a milky fluid found in 10% of all flowering plants (angiosperms ...

, for example, it is not primarily presentation-oriented. An OMDoc document need not specify what its contents should look like. A conversion to LaTeX and

XHTML Extensible HyperText Markup Language (XHTML) is part of the family of XML markup languages. It mirrors or extends versions of the widely used HyperText Markup Language (HTML), the language in which Web pages are formulated. While HTML, prior ...

(with Presentation

for the formulae) is possible, though. To this end, the presentation of each symbol can be defined.

Applications

Today, OMDoc is used in the following settings: ;

E-learning Educational technology (commonly abbreviated as edutech, or edtech) is the combined use of computer hardware, software, and Education sciences, educational theory and practice to facilitate learning. When referred to with its abbreviation, edt ...

:Creation of customized textbooks. ;Data exchange:OMDoc import and export modules are available for many automated theorem provers and

computer algebra system A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The de ...

s. OMDoc is intended to be used for communication between mathematical web services. ;Document preparation:Documents about mathematics can be prepared in OMDoc and later exported to a presentation-oriented format like LaTeX or XHTML+MathML.

History

OMDoc has been developed by the German mathematician and computer scientist

Michael Kohlhase Michael Kohlhase (born 13 September 1964, in Erlangen) is a Germans, German computer scientist and professor at University of Erlangen–Nuremberg, where he is head of the KWARC research group (Knowledge Adaptation and Reasoning for Content). Ac ...

since 1998. So far, there have been the following releases: * 1.0 (November 2000) * 1.1 (December 2001) * 1.2 (July 2006)

Future developments

It is planned to create the infrastructure for a “ semantic web for technology and science” based on OMDoc. To this end, OMDoc is being extended towards sciences other than mathematics. The first result is PhysML, an OMDoc variant extended towards

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

. For a better integration with other Semantic Web applications, an

OWL Owls are birds from the order Strigiformes (), which includes over 200 species of mostly solitary and nocturnal birds of prey typified by an upright stance, a large, broad head, binocular vision, binaural hearing, sharp talons, and feathers a ...

ontology of OMDoc is under development, as well as an export facility to RDF.

References

* Michael Kohlhase (2006):
An Open Markup Format for Mathematical Documents (Version 1.2)
'.

Lecture Notes in Artificial Intelligence ''Lecture Notes in Computer Science'' is a series of computer science books published by Springer Science+Business Media since 1973. Overview The series contains proceedings, post-proceedings, monographs, and Festschrifts. In addition, tutorial ...

, no. 4180.

Springer Verlag Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in ...

, Heidelberg. .

External links

*
Wiki for OMDoc and related projects
{{Authority control Markup languages Mathematical markup languages Semantic Web XML-based standards