=Paper=
{{Paper
|id=None
|storemode=property
|title=Authoring and Publishing of Units and Quantities in Semantic Documents
|pdfUrl=https://ceur-ws.org/Vol-721/paper-01.pdf
|volume=Vol-721
|dblpUrl=https://dblp.org/rec/conf/esws/CirlanaruG011
}}
==Authoring and Publishing of Units and Quantities in Semantic Documents==
https://ceur-ws.org/Vol-721/paper-01.pdf
Authoring and Publishing Units and Quantities
in Semantic Documents
Mihai Cîrlănaru, Deyan Ginev, Christoph Lange
Computer Science, Jacobs University Bremen, Germany
{m.cirlanaru,d.ginev,ch.lange}@jacobs-university.de
Abstract. This paper shows how an explicit representation of units
and quantities can improve the experience of semantically published
documents, and provides a first authoring method in this respect. To
exemplify the potential and practical advantages of encoding explicit
semantics regarding units w.r.t. user experience, we demonstrate a unit
system preference service, which enables the user to choose the system of
units for the displayed paper. By semantically publishing units, we obtain
a basis for a wide range of applications and services such as unknown
unit lookup, unit and quantity semantic search and unit and quantity
manipulation. Enabling semantic publishing for units is also presented
in the context of a large collection of legacy scientific documents (the
arXMLiv corpus), where our approach allows to non-invasively enrich
legacy publications.
1 Motivation
Units and quantities, although widely spread, lack a formal standard represen-
tation for semantic publishing. A multitude of problems [Usm] arise from the
different flavors (country specific unit standards) and formats (abbreviations,
special cases of occurrence) of units, making it hard for the untrained reader to
fully understand the information provided. Semantic publishing solves most such
problems by disambiguating the unit and quantity occurrences, which, further
on, will enable a wide range of applications and services to interact with them.
A unit is any determinate quantity, dimension, or magnitude adopted as a
basis or standard of measurement for other quantities of the same kind and in
terms of which their magnitude is calculated or expressed [Oxf], but from the
top-most level of perception, it simply provides information on a wide range
of quantifiable aspects. Concrete examples for the great extent of units and
quantities include cooking recipes, medical prescriptions, scientific papers and
many other. Semantic publishing can provide the middle layer that would ensure
a (automated) way of identifying and understanding these occurrences which can
enable the evolution of useful technologies and services.
At the perception level, aside from quantifying properties and relations
between objects, units bring the meaning of scale. Moreover, units have allowed
scientists to better transmit and exchange knowledge among themselves.
In real life, the misinterpretation of units and their quantities has often caused
accidents with harsh/expensive consequences. Consider losing a $125 million
satellite [Mar] because of the differences between metric and imperial unit systems,
or running out of fuel in mid-flight with an aircraft whose fuel sensors were faultily
configured in displaying the units [Air]. Fields like medicine, commerce, civil
engineering have also been marked by such types of errors and pitfalls [Usm].
This simply emphasizes the fact that units are frequently misinterpreted.
Providing semantics to units and their quantities for the publishing industry,
either by supplying semantic authoring tools or by semantically enriching their
occurrences in legacy documents, has high impact benefits. It will enable trans-
parent exchange of scientific knowledge between different academic communities,
typical of technical papers with high occurrence of units and quantities, and also
enhance the reader’s experience, via novel interactive services with day-to-day
published material, e.g. cooking recipes or technical manuals.
In the following sections the preliminaries (section 2) and state of the art
(section 4) for units and quantities are introduced in order to have a basis for
the unit and quantity interaction services (section 6) presented in this paper. We
outline immediate strategies (section 5) for extending the benefits of semantic
units to legacy documents (section 7) and conclude with a summary of our
mid-term outlook of future work (section 8).
2 Preliminaries
The core of semantic publishing resides in open and standardized markup lan-
guages used to encapsulate semantics. OpenMath and Content MathML are
the most widely used semantic markup (also called “content markup”) languages
for mathematical expressions, which are ubiquitous in science and engineering.
2.1 OpenMath and Content MathML
OpenMath [Bus+04] and the semantically equivalent Content MathML [Aus+10]
are standards for the representing the semantics of mathematical expressions
[KR09] – as annotations to visual renderings, or for the purpose of communi-
cation between computational services. Our investigations focus on these two
languages.1
Structurally, both OpenMath and MathML provide a valuable basis for
machine processing of mathematical expressions; they are ideal markup languages
for the purpose of semantic publishing of units and quantities. The expressivity
of MathML, provided by its vocabulary having close to 100 XML elements for
1
The prevalence of XML-based semantic markup languages for representing math-
ematical expressions – as opposed to RDF – has historical reasons but is also due
to the complex n-ary and ordered structures of mathematical expressions, which
are hard to break down into RDF triples. In both representations the vocabulary
terms (here: functions, operators, sets, constants) are identified by URIs. We refer to
[Lan11] for an in-depth treatment.
functions and operators for mathematics [KR09] and multiple unit and quantity
representation possibilities [DN03], and the modularity and extensibility of
OpenMath’s vocabulary by way of modular ontologies (“Content Dictionaries”,
abbreviated as CDs), enable the development of applications and services (some
of which are discussed in section 6.2) that build upon the semantic publishing of
units and quantities.
2.2 The Semantic Publishing Pipeline
Semantic Publishing, as a process, consists of at least three components, namely
authoring, publishing and interaction. Usually these processes imply three dif-
ferent groups of contributors – authors, publishers and readers. Incorporating
the full publishing lifecycle into a single system, striving for integration and
collaboration between the different participants, brings great benefits. In this
paper, we take the benefits of the social web for well-established2 and accepted
and focus on the more novel semantic aspects of the publishing realm. To this
extent, we develop our work in the context of the Planetary eMath3.0 system
(see [Koh+11] for an introduction). Notably, the Planetary framework imple-
ments the architecture introduced in [Dav+10] for publishing its documents as
XHTML+RDFa+MathML, enabling interactive semantic services.
In our work on units and quantities, we have concentrated on setting the
necessary technological foundation, hence building on the languages introduced
in section 2.1 to select and enhance the authoring and interaction aspects.
3 Semantic Units – Idea Outline
In order to understand how a semantic representation of units and quantities
will integrate with the publishing flow of our framework of choice, one first needs
to pinpoint what they comprise and how they are represented.
A computational semantic entity is an object with explicit structure, rep-
resentable in a machine-understandable form, and denoting a corresponding
real-world entity. The denotation is usually encoded via a machine-readable ontol-
ogy. This definition is directly applicable to semantic units and quantities, which
are exactly the machine-readable representations of their physical counterparts.
For the representation we choose OpenMath, since it encompasses units
through modular ontologies, called Content Dictionaries (CDs) [Col09], which
enable extensibility through the creation of new such ontologies that can add new
symbols or simply through the extension of the existing unit ontologies/CDs.
2
For mathematics, including the mathematical foundations of science and engineering,
see, e.g., the PlanetMath free encyclopedia [Pla] and the Polymath wiki/blog-based
collaboration effort [Bar10].
As a running example for this paper, we consider a semantic representation of
the physical quantity 100 km/h ; one possibility to represent it in OpenMath
is3 :
100
Listing 1.1. OpenMath representation of 100 km/h
4 State of the Art
We review the relevant prior work involving units and quantities in the context
of semantic publishing. Note that we do not cover the publishing dimension itself,
as it is a stand-alone framework level, independent of the processed content.
4.1 Representation
The semantic publishing aspect of units in scientific documents has not yet
accumulated a sizable body of prior work. Previous research has been mainly
concerned with the standardization of unit and quantity representation which is
far from complete (not covering every unit occurrence possibility) or sufficiently
machine comprehensible. There is a number of units-related semantic web ontolo-
gies: The authors of the Measurement Units Ontology [BP09] review a number
of ways of representing units in RDF. The SWEET ontology (Semantic Web
Earth and Environmental Terminology [Swe; RP05]) is particularly remarkable
for linking units to the fields of science where they occur. A general weakness of
RDF/OWL unit ontologies is, however, that the computation of derived units
(and thus unit conversion) cannot be described in a straightforward way (and is
rarely done).
For OpenMath, a representation of units and quantities has been proposed
(cf. [DN03]), and several CDs covering common units have been provided. The
3
This is one out of several ways of representing units (cf. [DN03]). For a detailed
description of the XML schema see section 3.1.2 of [Bus+04]
in-depth analysis of the prospective representations of units and their dimensions
that [DN03] proposes (taking into account the pros and cons of each approach)
allows for a broader view to the multitude of semantic publishing possibilities. The
two most significant sets of OpenMath unit CDs have been developed by James
Davenport and Jonathan Stratford [SD08] and Joseph Collins [Col09], respectively.
The former are remarkable for their explicit representation of conversion rules (see
also Section 4.3). The latter ones provide a standards-compliant implementation
of SI4 quantities and units, providing strong insight on the concepts of quantity
and unit and on the prospects of capturing more of their semantics in the
representation.
4.2 Authoring
In “pre-semantic” environments, such as LATEX, there are first approximations of
content-oriented macros that represent units. A prominent example is the LATEX
package SIunits [Hel] which covers the full range of base and derived units in
the SI system, as well as SI prefixes, a range of widely accepted units external to
SI and a couple of generic mechanisms for creating custom author-specified unit
constructs. The package enables a large set of abbreviative commands, which
are internally built up from the compositional application of atomic building
blocks. In this sense, the authoring process via SIunits is nearly semantic on the
interface level, but entirely presentational on the output side.
Still, all major semantic authoring systems (e.g. the semantic LATEX extensions
sTEX [Koh08], SALT [Gro+07], the Ontology Add-in for Microsoft Office Word
[Fin+10], or the semantic content management system PAUX [PAU]) have so
far neglected the specific use case of units. This can be partially explained by
the lack of a widely agreed standard representation, as well as different primary
development foci – mathematics for sTEX, rhetorical structures for SALT, life
sciences terminology for the Word ontology add-in, and educational texts from
areas unrelated to physics, such as law, for PAUX. Notably, sTEX could, in
principle, support units already, as its wide coverage of the conceptual model of
OpenMath and its generic mechanism for defining new symbols and concepts
could easily be utilized for the specification of the relevant unit and quantity
symbols. Section 5 presents how we have done that in a way that does not
disrupt existing LATEX authoring practices. While LATEX is commonly used in
mathematics, science, and engineering, our solution is unlikely to appeal to life
scientists, where Microsoft Office Word is more widely used; however, we leave
unit support for word processors to future work.
4.3 Interaction
Applications taking advantage of the semantic publishing of units and their
quantities using OpenMath have also been experimented with by various authors,
albeit the lack of authoring support. The unit conversion service [Str08; SD08]
4
The International System of Units [Sib]
by Jonathan Stratford, which users can easily extend by uploading new Content
Dictionaries (CDs) with new units and conversion rules, provides a good example
of the power of semantically annotated units. Besides the implementation of such
a service, Stratford’s research also identifies the difficulties of unit conversion and
the limitations of OpenMath’s current state with regard to unit representation.
Stratford’s conversion service is interactive in that users can enter quantities
into a web form and upload definitions of new units. We have additionally made
it interactively accessible from web documents that contain MathML formulas
with OpenMath annotations, as created by the publishing pipeline explained in
section 2.2 (cf. [GLR09]). This interaction with units in publications has, however,
remained a proof of concept so far, as producing suitably annotated documents
required manual authoring of quantity expressions in OpenMath XML markup
– a barrier that we are trying to overcome with the work presented in this paper.
5 Semantic Authoring of Units and Quantities
We have revised the available methods and technologies and established that a
semantic authoring support for units does not formally exist at present. Conse-
quently, we set out to make the first steps towards extending one of the more
prepared software solutions, namely sTEX, with a special authoring module for
units, by building on the existing pre-semantic toolbox of the SIunits LATEX
package. sTEX [Koh08] is essentially a collection of LATEX packages that offer
semantic macros. sTEX can be translated into XML markup using LaTeXML
[Mil] bindings, thus enabling easier subsequent processing – including semantic
web publishing (cf. [Dav+10]). Our units extension follows a similar approach5 .
As described in section 4.2, SIunits provides an sTEX-like content authoring
interface. For our running example, we are interested in authoring 100 km/h in
order to create the content representation shown in Listing 1.1. There are many
ways to author the representation in LATEX, e.g. via $\textrm{100\,km/h}$. The
SIunits package makes the process less ad-hoc by focusing on the content and
factoring out the presentational quirks, in the form of package options. Hence, one
would instead write the more semantic \unit{100}{\kilo\metre\per\hour}. It
is interesting to observe that a completely different motivation than ours, namely
to provide a convenient and centralized interface to control the presentation of
the unit entities on a document level, leads to the essentially same result which
we desire – a semantics-oriented authoring interface.
In our effort to leverage this functionality, we first created a LaTeXML
binding for the SIunits package. It helped us to pinpoint the semantic map
between the interface and the OpenMath representation and provided a non-
invasive semantic enrichment for LATEX documents based on the package. Next, we
use the gained understanding in building a native sTEX module for units, roughly
5
The SIunits bindings and sTeX extension will be released in the respective bundles
(the arXMLiv binding library and the sTeX package on CTAN) with the authors’
strong committment to free software licenses compatible with the originals.
based on the SIunits interface. Table 1 shows a small snippet comparing the
different stages. One easily notices the abbreviative power of the sTEX approach,
which hides the verbose and overly complex binding declaration under its hood,
exposing the author to a controlled LATEX vocabulary and facilitating reuse.
Language Definition Semantics
\ newcommand {\ kilo }{\ ensuremath {\ mathrm { k }}}
LATEX \ newcommand {\ metre }{\ ensuremath {\ mathrm { m }}} 7
DefC onstruct or ( ’\ kilo {} ’ , ’
< ltx : XMApp >
< ltx : XMTok meaning =" prefix " cd =" units_ops1 "/ >
< ltx : XMTok meaning =" kilo " cd =" un it s _s ip re f ix 1 " >
k
LaTeXML
#1 D
’) ;
DefC onstruct or ( ’\ metre ’ , ’
< ltx : XMTok meaning =" metre " cd =" units_metric1 " >
m
’) ;
\ symdef [ name = kilo , cd = u ni ts _s i pr ef ix 1 ]{ kiloPX }{\ mathrm { k }}
sTEX
\ symdef [ name = metre , cd = units_metric1 ]{ metre }{\ mathrm { m }}
\ symdef [ name = prefix , cd = u n it s_ si p re fi x1 ]{ prefixFN }{} D
\ symdef { kilo }[1]{\ mixfixii {}{\ kiloPX }{\ prefixFN }{#1}{}}
Table 1. Definitions for \kilo\metre, typeset as ‘km’
6 Interaction with Units and Quantities
Given the provisions for authoring support, we move to the added-value benefits
one could reap from interacting with a published document. This section details
relevant use cases and explains the prerequisites that are already available.
6.1 Unit (System) Preference Service
A concrete scenario for a prospective service that would take advantage of
semantically published papers, based on the ideas from section 3, can be evolved
on top of common published material like cooking recipes. These provide a good
use case thanks to the high density of units and quantities they contain. Moreover,
the physical quantities are restricted to a small subset (quantity/mass related
units) including special types of units [21c] which are not formally defined and
might prove to be misleading:
1 teaspoon (tsp) ≈ 5 millilitres (mL)
1 cup ≈ 250 millilitres (mL)
The idea of the unit (system) preference service is to allow the user/reader to
choose a preferred system of units (e.g. imperial, metric) or simply preferred types
of units (e.g. “minutes” instead of “hours”, “kilogrammes” instead of “grammes”)
for the representation of physical quantities and then seamlessly adapt the docu-
ment to these preferences. This can only be achieved at the end of the semantic
publishing pipeline, since the process requires the technologies described in sec-
tions 2 and 4 for the representation and authoring parts. Once these prerequisites
have been met, one can embed interactive scripts into the published document
(here: XHTML with OpenMath-annotated MathML formulae), which invoke a
web service for any computation. In our implementation, the JOBAD (Javascript
API for OMDoc-based Active Documents) framework [GLR09] provides for client-
server communication and manipulation of the document. Figure 1 visualizes the
workflow.
Fig. 1. Workflow for Chocolate Chip Cookies recipe [Crc]
6.2 Prospective Services based on Semantically Published Units
Having described in detail one service that enhances the user experience by pub-
lishing units semantically, we now list further potential services and applications
that the same technology could enable:
– Mapping Natural Sciences Concepts to their respective Units: defin-
ing Content Dictionaries that would describe the connection of units to general
natural sciences concepts like force (measured in Newtons: N = kgm s2 or any
2
variant of the ratio) or energy (measured in Joules: J = N m = kgm s2 = ...)
and plenty of other examples. The interconnection of concepts in sciences:
Energy = Force × displacement can further enable scientific formula “spell
checking” which might prove to be of great value to physicists, astronomers
and many others.
– Unknown Unit Lookup: In theoretical scientific papers authors usually
use abbreviations for concepts (e.g. N for Newtons – the unit for force)
without mentioning anything about units/dimensions, which might turn out
to be difficult for the readers who would be interested to know, for example,
the order of measurement (magnitude) for the unknown physical quantities
and also a (small) description of the respective concept (e.g. P a is the unit
for pressure). Defining a generic way in which semantics can be added to such
unknown symbols will enable showing/hiding units for expressions/formulas.
– Unit and Quantity Semantic Search: a library-level service that would
allow searching for units by their type, name and magnitude and return the
relevant results independently of the measuring standard of the occurrences
in the paper (e.g. imperial or metric) and also independent of their form (N
or kgm
s2 ).
6
– Quantity and Unit’s Magnitude Manipulation: a document interaction
service that is able to transform for example 100N → 0.1kN or 0.1 × 103 N or
2
0.1×103 kgm s2 . This can be useful when it comes to simplifying representations
and adapting them consistently to a certain type of magnitude (for example
all occurrences of force expressions should have their unit represented in kN ).
As detailed at the beginning of this paper, having a standard, uniform under-
standing of units and quantities can prevent hazards and even eliminate entire
compatibility check processes in industry. The presented list of prospective en-
abling technologies shows only a few of the numerous opportunities of interacting
with units and quantities in semantically published documents and serves as
strong motivation for future research in this direction.
7 Enabling Semantic Units in Legacy Corpora
The arXMLiv corpus is the ideal environment for the identification of units and
quantities since it contains a collection of more than 600,000 scientific publications.
It is based on Cornell University’s arXiv e-Print archive [Arx] originally typeset
in LATEX, converted to XML in order to achieve easy machine-readability, partial
semantics recovery and clear separation of document modalities such as natural
language and mathematical expressions [Sta+10]. Currently, the project has
achieved a successful conversion rate of nearly 70% to a semantically enriched
XHTML+MathML representation, natively understandable by modern web
browsers [Koh+08].
A proof-of-concept check, performed via the arXMLiv build system (see
[Sta+10]) revealed roughly 150 arXiv articles using the SIunits package, with an
outlook for close to tripling the number when considering sibling packages such as
units and SIunitx. This gives our work on creating a semantic binding for SIunits
an even stronger benefit, as we can directly and non-invasively enrich legacy
publications, putting them one step further on the path to semantic publishing.
An additional, mid-term benefit is the opportunity to build a linguistic Gold
Standard for units; we created both legacy (to presentational MathML) and
semantic (to OpenMath) bindings in order to provide a raw, presentational
6
In contrast, state-of-the-art scientific publication search services, such as Springer’s
LATEX search [Spr], do not support the semantics of units.
output and its annotated, semantic counterpart. Having both as a basis, unit
spotters can then be developed using methods of Computational Linguistics and
Machine Learning, further enriching the arXMLiv corpus.
Such enhancements not only enable the interactive services of semantic pub-
lishing on legacy corpora, but also provide a tempting outlook to the development
of an ecosystem of linguistic analysis modules, which can draw on the captured
semantics of units and quantities, as originally envisioned by the LaMaPUn
project [Gin+09].
8 Conclusions and Future Work
Units and quantities are sufficiently wide-spread and important to not be disre-
garded from the context of semantic documents. Unfortunately, by now, there
have been only isolated approaches (see section 4) to exploit the semantic power
of units. Also considering the wide range of existing unit types and representa-
tions, makes it almost impossible to identify and semantically enrich all of them,
especially when we are talking about occurrence contexts as unrelated as cooking
recipes, medical prescriptions, technical documents or scientific papers.
Through the separation of the semantic publishing process for units we
emphasized the importance of three major components: representation, authoring
and interaction, detailing technologies that can improve each of them. Moreover,
by providing a cooking recipe interaction use case and also a series of further
potential services and applications on top of semantically published units, we
contribute means of better manipulation and interpretation of units and quantities
to the Semantic Publishing Industry and to legacy corpora.
Acknowledgments: The authors would like to thank Michael Kohlhase for his
extensive support and advice regarding the writing of this paper, the anonymous
peer reviewers for their extensive helpful suggestions, and Anton Antonov for
writing the LaTeXML bindings for the SIunits LATEX package.
References
[21c] Code of Federal Regulations – Food and Drugs. 2004. url: http:
//edocket.access.gpo.gov/cfr_2004/aprqtr/21cfr101.9.htm.
[Air] Aviation Safety – Air Canada Accident Report. url: http : / /
aviation - safety . net / database / record . php ? id = 19830723 - 0
(visited on 10/25/2010).
[Arx] arxiv.org e-Print archive. url: http://www.arxiv.org.
[Aus+10] R. Ausbrooks et al. Mathematical Markup Language (MathML) Ver-
sion 3.0. Recommendation. W3C, 2010. url: http://www.w3.org/
TR/MathML3.
[Bar10] M. J. Barany. “‘[B]ut this is blog maths and we’re free to make
up conventions as we go along’: Polymath1 and the modalities of
‘massively collaborative mathematics’”. In: WikiSym. Ed. by P. Ayers
and F. Ortega. ACM Press. 2010.
[BP09] D. Berrueta and L. Polo. Measurement Units Ontology. Nov. 9, 2009.
url: http://forge.morfeo-project.org/wiki_en/index.php?
title=Measurement_Units_Ontology&oldid=12301.
[Bus+04] S. Buswell et al. Open Math Standard 2.0. Tech. rep. OpenMath
Society, 2004. url: http://www.openmath.org/standard/om20.
[Col09] J. B. Collins. “OpenMath Content Dictionaries for SI Quantities and
Units.” In: Calculemus/MKM. Ed. by J. Carette et al. Vol. 5625.
LNCS. Springer, 2009, pp. 247–262.
[Crc] Cooking.com – “Giant Chocolate Chip Cookies”. url: http://www.
cooking . com / recipes - and - more / recipes / Giant - Chocolate -
Chip-Cookies-recipe-5112.aspx (visited on 03/05/2011).
[Dav+10] C. David et al. “Publishing Math Lecture Notes as Linked Data”.
In: The Semantic Web: Research and Applications (Part II). Ed. by
L. Aroyo et al. LNCS 6089. Springer, 2010, pp. 370–375. arXiv:1004.
3390v1 [cs.DL].
[DN03] J. H. Davenport and W. A. Naylor. Units and Dimensions in Open-
Math. 2003. url: http://openmath.org/documents/Units.pdf.
[Fin+10] J. L. Fink et al. “Word add-in for ontology recognition: semantic
enrichment of scientific literature”. In: BMC Bioinformatics 11.103
(2010).
[Gin+09] D. Ginev et al. “An Architecture for Linguistic and Semantic Analysis
on the arXMLiv Corpus”. In: Applications of Semantic Technologies
(AST) Workshop at Informatik. 2009. url: http : // www . kwarc .
info/projects/lamapun/pubs/AST09_LaMaPUn+appendix.pdf.
[GLR09] J. Giceva, C. Lange, and F. Rabe. “Integrating Web Services into
Active Mathematical Documents”. In: MKM/Calculemus Proceedings.
Ed. by J. Carette et al. LNAI 5625. Springer, 2009, pp. 279–293.
[Gro+07] T. Groza et al. “SALT – Semantically Annotated LATEX for Scientific
Publications”. In: The Semantic Web: Research and Applications.
Ed. by E. Franconi, M. Kifer, and W. May. LNCS 4519. Springer,
2007, pp. 518–532.
[Hel] M. Heldoorn. The SIunits package: Consistent application of SI units.
url: http://mirror.ctan.org/macros/latex/contrib/SIunits/
SIunits.pdf (visited on 03/13/2011).
[Koh08] M. Kohlhase. “Using LATEX as a Semantic Markup Format”. In:
Mathematics in Computer Science 2.2 (2008), pp. 279–304. url:
https://svn.kwarc.info/repos/stex/doc/mcs08/stex.pdf.
[Koh+08] M. Kohlhase et al. “MathWebSearch 0.4, A Semantic Search Engine
for Mathematics”. manuscript. 2008. url: http://mathweb.org/
projects/mws/pubs/mkm08.pdf.
[Koh+11] M. Kohlhase et al. “The Planetary System: Web 3.0 & Active Docu-
ments for STEM”. In: accepted for publication at ICCS 2011 (Final-
ist at the Executable Papers Challenge). 2011. url: https://svn.
mathweb.org/repos/planetary/doc/epc11/paper.pdf.
[KR09] M. Kohlhase and F. Rabe. “Semantics of OpenMath and MathML3”.
In: 22nd OpenMath Workshop. Ed. by J. H. Davenport. 2009. url:
http://kwarc.info/kohlhase/papers/om09-semantics.pdf.
[Lan11] C. Lange. “Ontologies and Languages for Representing Mathematical
Knowledge on the Semantic Web”. accepted by Semantic Web Journal.
2011. url: http://www.semantic- web- journal.net/content/
new - submission - ontologies - and - languages - representing -
mathematical-knowledge-semantic-web.
[Mar] CNN – “NASAs metric confusion caused Mars orbiter loss”. 1999.
url: http://articles.cnn.com/1999- 09- 30/tech/9909_30_
mars.metric_1_mars- orbiter- climate- orbiter- spacecraft-
team?_s=PM:TECH (visited on 10/29/2010).
[Mil] B. Miller. LaTeXML: A LATEX to XML Converter. url: http://dlmf.
nist.gov/LaTeXML/ (visited on 03/03/2011).
[Oxf] Oxford English Dictionary. “unit” definition. url: http : / /
dictionary.oed.com/entrance.dtl (visited on 10/29/2010).
[PAU] PAUX Technologies. url: http://paux.de (visited on 10/10/2010).
[Pla] PlanetMath. url: http://planetmath.org (visited on 01/06/2011).
[RP05] R. G. Raskin and M. J. Pan. “Knowledge representation in the
semantic web for Earth environmental terminology (SWEET)”. In:
Computers & Geosciences 31 (2005), pp. 1119–1125.
[SD08] J. Stratford and J. H. Davenport. “Unit Knowledge Management”.
In: Intelligent Computer Mathematics. Ed. by S. Autexier et al. LNAI
5144. Springer, 2008, pp. 382–397.
[Sib] The International System of Units (SI) 8. Edition. Bureau Inter-
national des Poids et Mesures, 2006. url: http://www.bipm.org/
utils/common/pdf/si_brochure_8_en.pdf.
[Spr] Springer, ed. LATEX Search. url: http://www.latexsearch.com
(visited on 04/16/2011).
[Sta+10] H. Stamerjohanns et al. “Transforming large collections of scientific
publications to XML”. In: Mathematics in Computer Science 3.3
(2010): Special Issue on Authoring, Digitalization and Management
of Mathematical Knowledge. Ed. by S. Autexier, P. Sojka, and M.
Suzuki, pp. 299–307. url: http://kwarc.info/kohlhase/papers/
mcs10.pdf.
[Str08] J. Stratford. Creating an extensible Unit Converter using OpenMath
as the Representation of the Semantics of the Units. Tech. rep. 2008-
02. University of Bath, 2008. url: http://www.cs.bath.ac.uk/
pubdb/download.php?resID=290.
[Swe] Semantic Web for Earth and Environmental Terminology (SWEET).
NASA. url: http://sweet.jpl.nasa.gov/ (visited on 08/22/2010).
[Usm] US Metric Association “Unit Mixups” article. url: http : / /
lamar.colostate.edu/~hillger/unit- mixups.html (visited on
10/25/2010).