SWAIE presentation on the Ontology of units of Measure

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IDENTIFYING AND EXTRACTING QUANTITATIVE DATA IN ANNOTATED TEXT

Don Willems, Hajo Rijgersberg, and Jan Top

OM-LATEX

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UNITS and QUANTITIES

Length (l)

metre (m)

Unit of measurement★ a definite magnitude of a ‘physical’ quantity★ used as a standard

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Unit of measurement★ a definite magnitude of a ‘physical’ quantity★ used as a standard★ used for the measurement of the same quantity

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l = 0.589 x 1m

l = 0.091 x 1m

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l = 58.9 cm

l = 9.1 cm

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l = 1.93 ft

l = 3.6 in

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l = 1.91x10-17 pc

l = 9.1x108 Å

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AMBIGUITY

Second

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AMBIGUITY

Second

Second of time(s)the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom

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AMBIGUITY

Second


Second of arc (’’)1/3600 of 1° or 8/100.000.000 of a full circle

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AMBIGUITY

Second


Sidereal second (s)1/86400 of a sidereal day, the rotation period of the Earth. 1 sidereal second = 0.9972696 seconds of time

Second of arc (’’)1/3600 of 1° or 8/100.000.000 of a full circle

Second (hour angle) (s)1/240 of 1° or 1/100.000 of a full circle

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AMBIGUITY

M

UnitUnitUnitUnitUnit

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AMBIGUITY

M

Moment of Force

Molar Mass

Absolute Magnitude Luminous Exitance

Magnetic QuantumNumber

UnitUnitUnitUnitUnit

Magnetisation

Mutual Inductance

Radiant Exitance

Quantum number of component of J in the direction of an external field

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GOALDisambiguation of Units and Quantities

Easy Annotation in LATEX

Correct Formatting of Units and Quantities

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OUTLINE

Ontology

OM - LATEX

Annotations

Conclusions

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ONTOLOGY of UNITS of MEASUREOntology OM - LaTeX Annotations Conclusions

The ontology of units of Measure★ implements a shared, formal vocabulary ★ uses RDF and OWL★ focusses on elementary concepts of quantitative

knowledge, for instance on:★ Units of measure★ Quantities★ Measurement Scales

★ based on a semi-formal description of the domain extracted from textual descriptions:

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ONTOLOGY of UNITS of MEASURE - sourcesOntology OM - LaTeX Annotations Conclusions

★ E.R. Cohen, P. Giacomo, Symbols, Units, Nomenclature and Fundamental Constants, 1987

★ R.C. Weast (Ed.), The CRC Handbook of Chemistry and Physics, 1976

★ B.N. Taylor, Guide for the use of the International System of Units, 1995

★ The NIST Reference on Constants, Units, and Uncertainty, 2004

★ P. Kenneth Seidelmann (Ed.), Explanatory Supplement to the Astronomical Almanac, 1992

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ONTOLOGY of UNITS of MEASURE - structureOntology OM - LaTeX Annotations Conclusions

PrefixCLASS

Unit of measureCLASS

System of unitsCLASS

QuantityCLASS

Measurement scaleCLASS

DimensionCLASS

MeasureCLASS

numerical value (Float)

pre

fix

unit

of

mea

sure unit of measure mea

sure

ment s

cale

dim

ensi

on

derived quantity

base quantitybase

unit

derived

unit

definition

unit of measure

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ONTOLOGY of UNITS of MEASURE - structureOntology OM - LaTeX Annotations Conclusions

om:unit_of_measure_

or_measurement_scale

om:num

erical_value

15.2DOUBLE

mm:_15.2_NINSTANCE

mq:forceINSTANCE

om:newtonINSTANCE

om:Singular_unitCLASS

om:ForceCLASS

om:MeasureCLASS

rdfs:ty

pe

om:value

rdfs:ty

pe

rdfs:ty

pe

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ONTOLOGY of UNITS of MEASURE - comparissonOntology OM - LaTeX Annotations Conclusions

OntologyOntologyOntologyOntologyOntologyOntology

Concept or relation EngMath SUMO ScadaOnWeb SWEET Unit OpenMath OM

Unit of Measure ✔ ✔ ✔ ✔ ✔

Prefix ✔ ✔ ✔ ✔

Quantity ✔ ✔ ✔ ✔

Measurement Scale ✔ ✔

Measure ✔ ✔

System of Units ✔ ✔

Dimension ✔ ✔ ✔ ✔

Quantities formally refer to units ✔ ✔ ✔ ✔ ✔

Units of measure have formal definitions in terms of other units ✔ ✔ ✔ ✔ ✔ ✔

Multiples and submultiples of units refer to predefined prefixes ✔ ✔ ✔

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ONTOLOGY of UNITS of MEASURE - applicationsOntology OM - LaTeX Annotations Conclusions

★ Many ontologies are not reused★ Created with no application in mind★ Number of applications very poor

★ OM★ Web applications★ OM Excel Add-in

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OM-LATEXOntology OM - LaTeX Annotations Conclusions

LaTeX★ Typesetting (the creation of a visual representation of

text)★ Uses high-level commands★ users do not have to worry about typography

★ Can be easily extended with new commands★ Used often in physical sciences★ Very powerful mathematical typesetting

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of information that are often used. These commands are either defined in the mainLATEX source file or in style files which can be imported into the main LATEX file.

In this paper we present a LATEX package (as a set of style files) that uses terminol-ogy as offered through our ontology platform wurvoc.org.

3.1 Ontology of units of Measure and related concepts (OM)

The ontology that we use to refer to in the LATEX files is OM. OM is an ontology basedon older ontologies of units of measure, such as EngMath by Tom Gruber [18]. Inearlier work [16] we have compared OM, EngMath and other ontologies, and OM ap-peared to be the most extended ontology, e.g. defining the most of the relevant con-cepts in the quantitative domain, such as “quantity”, “unit of measure”, “dimension”,“measure”, “measurement scale”, etc.

OM defines concepts such as unit, quantity and dimension. Quantities are re-lated to units of measure and measurement scales that can be used to express themusing the relation \unit_of_measure. Units of measure are defined by some observ-able standard phenomenon, such as the length of the path travelled by light in a vac-uum during a time interval of 1/299 792 458 of a second, for meter. Measures, suchas “3 kilogram” are used to indicate values of quantities. Multiples and submultiplesof units have a prefix, such as in kilogram and millimetre.

Systems of units organise quantities and units of measure, e.g. the InternationalSystem of Units (SI). Such a system defines base units and derived units. Base unitsare units that cannot be defined in terms of other units (e.g. metre and second).Base units can be combined into derived units, such as for example metre per sec-ond (ms°1).

OM is based on a semi-formal description of the domain of units of measure,drafted from several paper standards that we have analysed, e.g. the Guide for theUse of the International System of Units [19], by the NIST. For a full list of statements,the sources that we have used, and ontological choices made, see previous work [16].

OM is modelled in OWL 2 [20]. The ontology is published as Linked Open Data [21]through our vocabulary and ontology portal wurvoc.3 OM can be used freely underthe Creative Commons 3.0 Netherlands license.

3.2 Aliases in LATEX

When using LATEX it is often preferable to create aliases for often used (complex) com-mand structures instead of retyping these command structures again and again.

For instance, LATEX source code becomes more difficult to interpret when unitsare used in an equation. To create a statement like:

G = 6.673£10°11 Nm2 kg°2 (1)

which is the gravitational constant, the following LATEX source code can be used:

3 http://www.wurvoc.org/vocabularies/om-1.8/. The objective of wurvoc.org is to publishvocabularies and associated web services relevant to the general domain of physical unitsand quantities and in particular the domains of life sciences and agrotechnology. In wurvocone can browse vocabularies and directly interface with them.

G = 6.673\times 10^{-11} \mathrm{N} \mathrm{m^2} \mathrm{kg^{-2}}

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\newcommand{\Gunit}{\mathrm{N} \mathrm{m^2} \mathrm{kg^{-2}}}

\newcommand{\E}[1]{\times10^{#1}}

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G = 6.673£10°11 Nm2 kg°2 (1)



G = 6.673\times 10^{-11} \mathrm{N} \mathrm{m^2} \mathrm{kg^{-2}}

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G = 6.673£10°11 Nm2 kg°2 (1)



G = 6.673\E{-11} \GUnit

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OM-LATEX - typesettingOntology OM - LaTeX Annotations Conclusions

Dieudonné Willems AA2051- Question Sheet 2 October 6, 2012

Using the values given we get:

NH2 = 4£104 MØ2.0£1.660£10°27 kg

(24)

= 8£1034 kg2.0£1.660£10°27 kg

(25)

= 2.4£1061 (26)

NHe = 1£104 MØ4.0£1.660£10°27 kg

(27)

= 2£1034 kg4.0£1.660£10°27 kg

(28)

= 3.0£1060 (29)

m = 8£1034 kg+2£1034 kg2.4£1061 +3.0£1060 (30)

= 10£1034 kg2.7£1061 (31)

= 3.7£10°27 kg (32)

= 2.2a.m.u. (33)

The Jeans mass is given by Equation 3.11 in the course notes:

MJ =µºkTµmH G

∂ 32Ω° 1

2 (34)

where T = 170K is the temperature of the GMC, µmH = m = 3.7£ 10°27 kg is the mean mass, andΩ = 5.0£10°20 kgm°3 is the (uniform) density. This gives a Jeans mass of:

MJ =µ

3.1416£1.381£10°23 JK°1 £170K3.7£10°27 kg£6.673£10°11 Nm2 kg°2

∂ 32

££5.0£10°20 kgm°3§° 1

2 (35)

=°2.987£1016¢ 3

2 ££5.0£10°20§° 1

2 (36)

= 5.163£1024 £4.5£109 (37)

= 2.3£1034 kg (38)

= 1.2£104 MØ (39)

ii) If the cloud is supported only by its thermal kinetic energy, will it be stable or will itcollapse?If the GMC is only supported by its thermal kinetic energy, it will collapse if the mass of the cloud islarger than the critical mass, the Jeans mass (see course notes, page 3.18). The mass of the cloud isMGMC = mH2 +mHe = 5£104 MØ. The mass of the GMC is larger than the Jeans mass, it will thereforecollapse if it is only supported by its thermal energy.

d) Suppose now that the cloud also has bulk turbulence and magnetic field such thatthere is equipartition of energy, ©=Um = J .

i) Calculate the critical mass for collapse in this case.

4



NH2 = 4£104 MØ2.0£1.660£10°27 kg

(24)

= 8£1034 kg2.0£1.660£10°27 kg

(25)

= 2.4£1061 (26)

NHe = 1£104 MØ4.0£1.660£10°27 kg

(27)

= 2£1034 kg4.0£1.660£10°27 kg

(28)

= 3.0£1060 (29)

m = 8£1034 kg+2£1034 kg2.4£1061 +3.0£1060 (30)

= 10£1034 kg2.7£1061 (31)

= 3.7£10°27 kg (32)

= 2.2a.m.u. (33)


MJ =µºkTµmH G

∂ 32Ω° 1

2 (34)


MJ =µ

3.1416£1.381£10°23 JK°1 £170K3.7£10°27 kg£6.673£10°11 Nm2 kg°2

∂ 32

££5.0£10°20 kgm°3§° 1

2 (35)

=°2.987£1016¢ 3

2 ££5.0£10°20§° 1

2 (36)

= 5.163£1024 £4.5£109 (37)

= 2.3£1034 kg (38)

= 1.2£104 MØ (39)




4

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Quantities: Italics Subscripts are not in italics except when they refer to another quantity




NH2 = 4£104 MØ2.0£1.660£10°27 kg

(24)

= 8£1034 kg2.0£1.660£10°27 kg

(25)

= 2.4£1061 (26)

NHe = 1£104 MØ4.0£1.660£10°27 kg

(27)

= 2£1034 kg4.0£1.660£10°27 kg

(28)

= 3.0£1060 (29)

m = 8£1034 kg+2£1034 kg2.4£1061 +3.0£1060 (30)

= 10£1034 kg2.7£1061 (31)

= 3.7£10°27 kg (32)

= 2.2a.m.u. (33)


MJ =µºkTµmH G

∂ 32Ω° 1

2 (34)


MJ =µ

3.1416£1.381£10°23 JK°1 £170K3.7£10°27 kg£6.673£10°11 Nm2 kg°2

∂ 32

££5.0£10°20 kgm°3§° 1

2 (35)

=°2.987£1016¢ 3

2 ££5.0£10°20§° 1

2 (36)

= 5.163£1024 £4.5£109 (37)

= 2.3£1034 kg (38)

= 1.2£104 MØ (39)




4



NH2 = 4£104 MØ2.0£1.660£10°27 kg

(24)

= 8£1034 kg2.0£1.660£10°27 kg

(25)

= 2.4£1061 (26)

NHe = 1£104 MØ4.0£1.660£10°27 kg

(27)

= 2£1034 kg4.0£1.660£10°27 kg

(28)

= 3.0£1060 (29)

m = 8£1034 kg+2£1034 kg2.4£1061 +3.0£1060 (30)

= 10£1034 kg2.7£1061 (31)

= 3.7£10°27 kg (32)

= 2.2a.m.u. (33)


MJ =µºkTµmH G

∂ 32Ω° 1

2 (34)


MJ =µ

3.1416£1.381£10°23 JK°1 £170K3.7£10°27 kg£6.673£10°11 Nm2 kg°2

∂ 32

££5.0£10°20 kgm°3§° 1

2 (35)

=°2.987£1016¢ 3

2 ££5.0£10°20§° 1

2 (36)

= 5.163£1024 £4.5£109 (37)

= 2.3£1034 kg (38)

= 1.2£104 MØ (39)




4

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Quantities: Italics Subscripts are not in italics except when they refer to another quantity

Units: No italics




NH2 = 4£104 MØ2.0£1.660£10°27 kg

(24)

= 8£1034 kg2.0£1.660£10°27 kg

(25)

= 2.4£1061 (26)

NHe = 1£104 MØ4.0£1.660£10°27 kg

(27)

= 2£1034 kg4.0£1.660£10°27 kg

(28)

= 3.0£1060 (29)

m = 8£1034 kg+2£1034 kg2.4£1061 +3.0£1060 (30)

= 10£1034 kg2.7£1061 (31)

= 3.7£10°27 kg (32)

= 2.2a.m.u. (33)


MJ =µºkTµmH G

∂ 32Ω° 1

2 (34)


MJ =µ

3.1416£1.381£10°23 JK°1 £170K3.7£10°27 kg£6.673£10°11 Nm2 kg°2

∂ 32

££5.0£10°20 kgm°3§° 1

2 (35)

=°2.987£1016¢ 3

2 ££5.0£10°20§° 1

2 (36)

= 5.163£1024 £4.5£109 (37)

= 2.3£1034 kg (38)

= 1.2£104 MØ (39)




4



NH2 = 4£104 MØ2.0£1.660£10°27 kg

(24)

= 8£1034 kg2.0£1.660£10°27 kg

(25)

= 2.4£1061 (26)

NHe = 1£104 MØ4.0£1.660£10°27 kg

(27)

= 2£1034 kg4.0£1.660£10°27 kg

(28)

= 3.0£1060 (29)

m = 8£1034 kg+2£1034 kg2.4£1061 +3.0£1060 (30)

= 10£1034 kg2.7£1061 (31)

= 3.7£10°27 kg (32)

= 2.2a.m.u. (33)


MJ =µºkTµmH G

∂ 32Ω° 1

2 (34)


MJ =µ

3.1416£1.381£10°23 JK°1 £170K3.7£10°27 kg£6.673£10°11 Nm2 kg°2

∂ 32

££5.0£10°20 kgm°3§° 1

2 (35)

=°2.987£1016¢ 3

2 ££5.0£10°20§° 1

2 (36)

= 5.163£1024 £4.5£109 (37)

= 2.3£1034 kg (38)

= 1.2£104 MØ (39)




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OM-LATEX - packageOntology OM - LaTeX Annotations Conclusions

OM-LaTeX★ Generated automatically from the Ontology★ Includes hyperlinks with the relevant URI★ Defines commands for units and quantities in OM★ om:metre becomes \metre★ om:Molar_heat_capacity becomes

\MolarHeatCapacity

★ Includes correct typesetting★ \MagnetomotiveForce becomes

ONTOLOGY OF MEASURES LATEX PACKAGES 47

LATEX command: \MagnetizationURI: om:Magnetization

magnetomotive forceMagnetomotive force at a point is the work that is required to bring unit positive pole from an infinite distance (zero

potential) to the point.

Symbol: Fm

LATEX command: \MagnetomotiveForceURI: om:Magnetomotive_force

mutual inductanceSymbol: M

LATEX command: \MutualInductanceURI: om:Mutual_inductance

permeability of free spaceSymbol: µ

LATEX command: \PermeabilityOfFreeSpace or \VacuumPermeabilityURI: om:Permeability_of_free_space

permittivitySymbol: ≤

LATEX command: \PermittivityURI: om:Permittivity

potential differenceSymbol: U

LATEX command: \PotentialDifferenceURI: om:Potential_difference

http://www.wurvoc.org/vocabularies/om-1.8/Molar_heat_capacity

http://www.wurvoc.org/vocabularies/om-1.8/Molar_heat_capacity

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NH2 = 4£104 MØ2.0£1.660£10°27 kg

(24)

= 8£1034 kg2.0£1.660£10°27 kg

(25)

= 2.4£1061 (26)

NHe = 1£104 MØ4.0£1.660£10°27 kg

(27)

= 2£1034 kg4.0£1.660£10°27 kg

(28)

= 3.0£1060 (29)

m = 8£1034 kg+2£1034 kg2.4£1061 +3.0£1060 (30)

= 10£1034 kg2.7£1061 (31)

= 3.7£10°27 kg (32)

= 2.2a.m.u. (33)


MJ =µºkTµmH G

∂ 32Ω° 1

2 (34)


MJ =µ

3.1416£1.381£10°23 JK°1 £170K3.7£10°27 kg£6.673£10°11 Nm2 kg°2

∂ 32

££5.0£10°20 kgm°3§° 1

2 (35)

=°2.987£1016¢ 3

2 ££5.0£10°20§° 1

2 (36)

= 5.163£1024 £4.5£109 (37)

= 2.3£1034 kg (38)

= 1.2£104 MØ (39)




4



NH2 = 4£104 MØ2.0£1.660£10°27 kg

(24)

= 8£1034 kg2.0£1.660£10°27 kg

(25)

= 2.4£1061 (26)

NHe = 1£104 MØ4.0£1.660£10°27 kg

(27)

= 2£1034 kg4.0£1.660£10°27 kg

(28)

= 3.0£1060 (29)

m = 8£1034 kg+2£1034 kg2.4£1061 +3.0£1060 (30)

= 10£1034 kg2.7£1061 (31)

= 3.7£10°27 kg (32)

= 2.2a.m.u. (33)


MJ =µºkTµmH G

∂ 32Ω° 1

2 (34)


MJ =µ

3.1416£1.381£10°23 JK°1 £170K3.7£10°27 kg£6.673£10°11 Nm2 kg°2

∂ 32

££5.0£10°20 kgm°3§° 1

2 (35)

=°2.987£1016¢ 3

2 ££5.0£10°20§° 1

2 (36)

= 5.163£1024 £4.5£109 (37)

= 2.3£1034 kg (38)

= 1.2£104 MØ (39)




4

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NH2 = 4£104 MØ2.0£1.660£10°27 kg

(24)

= 8£1034 kg2.0£1.660£10°27 kg

(25)

= 2.4£1061 (26)

NHe = 1£104 MØ4.0£1.660£10°27 kg

(27)

= 2£1034 kg4.0£1.660£10°27 kg

(28)

= 3.0£1060 (29)

m = 8£1034 kg+2£1034 kg2.4£1061 +3.0£1060 (30)

= 10£1034 kg2.7£1061 (31)

= 3.7£10°27 kg (32)

= 2.2a.m.u. (33)


MJ =µºkTµmH G

∂ 32Ω° 1

2 (34)


MJ =µ

3.1416£1.381£10°23 JK°1 £170K3.7£10°27 kg£6.673£10°11 Nm2 kg°2

∂ 32

££5.0£10°20 kgm°3§° 1

2 (35)

=°2.987£1016¢ 3

2 ££5.0£10°20§° 1

2 (36)

= 5.163£1024 £4.5£109 (37)

= 2.3£1034 kg (38)

= 1.2£104 MØ (39)




4



NH2 = 4£104 MØ2.0£1.660£10°27 kg

(24)

= 8£1034 kg2.0£1.660£10°27 kg

(25)

= 2.4£1061 (26)

NHe = 1£104 MØ4.0£1.660£10°27 kg

(27)

= 2£1034 kg4.0£1.660£10°27 kg

(28)

= 3.0£1060 (29)

m = 8£1034 kg+2£1034 kg2.4£1061 +3.0£1060 (30)

= 10£1034 kg2.7£1061 (31)

= 3.7£10°27 kg (32)

= 2.2a.m.u. (33)


MJ =µºkTµmH G

∂ 32Ω° 1

2 (34)


MJ =µ

3.1416£1.381£10°23 JK°1 £170K3.7£10°27 kg£6.673£10°11 Nm2 kg°2

∂ 32

££5.0£10°20 kgm°3§° 1

2 (35)

=°2.987£1016¢ 3

2 ££5.0£10°20§° 1

2 (36)

= 5.163£1024 £4.5£109 (37)

= 2.3£1034 kg (38)

= 1.2£104 MØ (39)




4

\JeansMass = 1.2\E{4} \solarMass

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OM-LATEX - annotationsOntology OM - LaTeX Annotations Conclusions



NH2 = 4£104 MØ2.0£1.660£10°27 kg

(24)

= 8£1034 kg2.0£1.660£10°27 kg

(25)

= 2.4£1061 (26)

NHe = 1£104 MØ4.0£1.660£10°27 kg

(27)

= 2£1034 kg4.0£1.660£10°27 kg

(28)

= 3.0£1060 (29)

m = 8£1034 kg+2£1034 kg2.4£1061 +3.0£1060 (30)

= 10£1034 kg2.7£1061 (31)

= 3.7£10°27 kg (32)

= 2.2a.m.u. (33)


MJ =µºkTµmH G

∂ 32Ω° 1

2 (34)


MJ =µ

3.1416£1.381£10°23 JK°1 £170K3.7£10°27 kg£6.673£10°11 Nm2 kg°2

∂ 32

££5.0£10°20 kgm°3§° 1

2 (35)

=°2.987£1016¢ 3

2 ££5.0£10°20§° 1

2 (36)

= 5.163£1024 £4.5£109 (37)

= 2.3£1034 kg (38)

= 1.2£104 MØ (39)




4



NH2 = 4£104 MØ2.0£1.660£10°27 kg

(24)

= 8£1034 kg2.0£1.660£10°27 kg

(25)

= 2.4£1061 (26)

NHe = 1£104 MØ4.0£1.660£10°27 kg

(27)

= 2£1034 kg4.0£1.660£10°27 kg

(28)

= 3.0£1060 (29)

m = 8£1034 kg+2£1034 kg2.4£1061 +3.0£1060 (30)

= 10£1034 kg2.7£1061 (31)

= 3.7£10°27 kg (32)

= 2.2a.m.u. (33)


MJ =µºkTµmH G

∂ 32Ω° 1

2 (34)


MJ =µ

3.1416£1.381£10°23 JK°1 £170K3.7£10°27 kg£6.673£10°11 Nm2 kg°2

∂ 32

££5.0£10°20 kgm°3§° 1

2 (35)

=°2.987£1016¢ 3

2 ££5.0£10°20§° 1

2 (36)

= 5.163£1024 £4.5£109 (37)

= 2.3£1034 kg (38)

= 1.2£104 MØ (39)




4

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OM-LATEX - annotationsOntology OM - LaTeX Annotations Conclusions

om:Jeans_mass

om:solar_mass



NH2 = 4£104 MØ2.0£1.660£10°27 kg

(24)

= 8£1034 kg2.0£1.660£10°27 kg

(25)

= 2.4£1061 (26)

NHe = 1£104 MØ4.0£1.660£10°27 kg

(27)

= 2£1034 kg4.0£1.660£10°27 kg

(28)

= 3.0£1060 (29)

m = 8£1034 kg+2£1034 kg2.4£1061 +3.0£1060 (30)

= 10£1034 kg2.7£1061 (31)

= 3.7£10°27 kg (32)

= 2.2a.m.u. (33)


MJ =µºkTµmH G

∂ 32Ω° 1

2 (34)


MJ =µ

3.1416£1.381£10°23 JK°1 £170K3.7£10°27 kg£6.673£10°11 Nm2 kg°2

∂ 32

££5.0£10°20 kgm°3§° 1

2 (35)

=°2.987£1016¢ 3

2 ££5.0£10°20§° 1

2 (36)

= 5.163£1024 £4.5£109 (37)

= 2.3£1034 kg (38)

= 1.2£104 MØ (39)




4



NH2 = 4£104 MØ2.0£1.660£10°27 kg

(24)

= 8£1034 kg2.0£1.660£10°27 kg

(25)

= 2.4£1061 (26)

NHe = 1£104 MØ4.0£1.660£10°27 kg

(27)

= 2£1034 kg4.0£1.660£10°27 kg

(28)

= 3.0£1060 (29)

m = 8£1034 kg+2£1034 kg2.4£1061 +3.0£1060 (30)

= 10£1034 kg2.7£1061 (31)

= 3.7£10°27 kg (32)

= 2.2a.m.u. (33)


MJ =µºkTµmH G

∂ 32Ω° 1

2 (34)


MJ =µ

3.1416£1.381£10°23 JK°1 £170K3.7£10°27 kg£6.673£10°11 Nm2 kg°2

∂ 32

££5.0£10°20 kgm°3§° 1

2 (35)

=°2.987£1016¢ 3

2 ££5.0£10°20§° 1

2 (36)

= 5.163£1024 £4.5£109 (37)

= 2.3£1034 kg (38)

= 1.2£104 MØ (39)




4

COMMIT/ E-FOODLAB


Each command has an optional parameter★ Without parameter in math mode:

★ \RelativePressureCoefficient results in:

★ With parameter in math mode:

★ \RelativePressureCoefficient[c_p] results in:

★ With parameter in text mode:

★ \RelativePressureCoefficient[coefficient] results in:

★ All annotated with the same URI

Æp

cp

coefficient

1

Æp

cp

coefficient

1

Æp

cp

coefficient

1

COMMIT/ E-FOODLAB


Each command has an optional parameter★ Without parameter in math mode:

★ \RelativePressureCoefficient results in:

★ With parameter in math mode:

★ \RelativePressureCoefficient[c_p] results in:

★ With parameter in text mode:

★ \RelativePressureCoefficient[coefficient] results in:

★ All annotated with the same URI

Æp

cp

coefficient

1

Æp

cp

coefficient

1

Æp

cp

coefficient

1

om:Relative_pressure_coefficient

COMMIT/ E-FOODLAB

OM-LATEX - comparison with SIUnitsOntology OM - LaTeX Annotations Conclusions

LaTeX PackageLaTeX Package

SIUnits OM-LaTeX

SI Units ✔ ✔

Derived units ✔ * ✔

Other units ✔

Prefixes ✔ * ✔

Quantities ✔

Semantic Annotations ✔

Total number of commands for units 92 ~1000Total number of commands for quantities ~500

* uses multiple commands to present prefixes and derived unitse.g. \kilo\metre\per\second

COMMIT/ E-FOODLAB

ANNOTATIONS Ontology OM - LaTeX Annotations Conclusions

Annotations:★ Disambiguate units and quantities in text or in

symbols.★ Make the information available for:★ conversion of the quantity to other units,★ dimensional analysis of equations,★ reasoning.

COMMIT/ E-FOODLAB

All LATEX commands representing quantities and units can also be used with userdefined symbols simply by adding an (optional) parameter to a command. For in-stance, the command \LuminousFlux produces the symbol for the quantity lumi-nous flux ’F ’ with a link to the related concept (om:Lumious_flux) in the OM ontol-ogy. If the author wants to use another symbol to represent luminous flux, he or shecan achieve this by specifying the alternative symbol as an argument:\LuminousFlux[\Phi] produces ’©’, still linked with the same concept in the OMontology. If desired sub- and superscripts can also be used in the argument:\LuminousFlux[F_{\lambda}] produces ’F∏’, again linked with the same URI.

3.4 URI and equation extraction

When using the typesetting tool pdflatex to create PDF files from the LATEX source,the URIs representing the unit and quantity concepts are inserted as hyperlinks intothe PDF. To use these annotations we have to parse the PDF files to find the hyper-links (URIs). Using Apache’s PDFBox http://pdfbox.apache.org/ we were able tocreate a small Java tool to parse the PDF files and extract the URIs representing con-cepts in OM and linking these URIs to the text.

Using this setup we are able to extract OM concepts (units and quantities) from atext generated with OM-annotated LATEX. We would, however, also like to extract thesemantics of statements like V = 15.2m3 (i.e. we would like to extract the fact thatthe quantity volume has a value of 15.2 in units of cubic metre). To this end we havealso added the functionality of finding binary (=, <, >, º, etc.) relations in the text tothe extraction tool.

When a PDF is parsed by the extraction tool, URIs for units and quantities, nu-meric values and binary relations are tagged in the text. Operators, like \E are alsorecognised, and in the case of exponents, the value is changed accordingly (e.g. 5.2£103 is changed to 5200). The tool then applies rules to find patterns in the text like:

[QUANTITY] [BINARY_RELATION] [VALUE] [UNIT]

If the tool comes across such a pattern, the combination of quantity, relation, value,and unit is stored. For instance the equation:

Ek = 1.209£10°2 eV (3)

is extracted as:

1 [QUANTITY=om:Kinetic_energy] [BINARY_RELATION=’=’]2 [VALUE=�.�12�9] [UNIT=om:electronvolt]

In this manner quantitative statements can be extracted from PDF generated withOM annotated LATEX.

3.5 Transformation to RDF

The result of the extraction can then be transformed into RDF statements using theOM ontology. For instance, the following equation

F = 15.2N (4)

ANNOTATIONS - parsingOntology OM - LaTeX Annotations Conclusions

pdflatex produces PDF with URIs as annotations★ The PDF can be parsed using a rule-based tool★ Searches for pattern:


COMMIT/ E-FOODLAB

QUANTITY BINARY RELATION VALUE UNIT

All LATEX commands representing quantities and units can also be used with userdefined symbols simply by adding an (optional) parameter to a command. For in-stance, the command \LuminousFlux produces the symbol for the quantity lumi-nous flux ’F ’ with a link to the related concept (om:Lumious_flux) in the OM ontol-ogy. If the author wants to use another symbol to represent luminous flux, he or shecan achieve this by specifying the alternative symbol as an argument:\LuminousFlux[\Phi] produces ’©’, still linked with the same concept in the OMontology. If desired sub- and superscripts can also be used in the argument:\LuminousFlux[F_{\lambda}] produces ’F∏’, again linked with the same URI.

3.4 URI and equation extraction

When using the typesetting tool pdflatex to create PDF files from the LATEX source,the URIs representing the unit and quantity concepts are inserted as hyperlinks intothe PDF. To use these annotations we have to parse the PDF files to find the hyper-links (URIs). Using Apache’s PDFBox http://pdfbox.apache.org/ we were able tocreate a small Java tool to parse the PDF files and extract the URIs representing con-cepts in OM and linking these URIs to the text.

Using this setup we are able to extract OM concepts (units and quantities) from atext generated with OM-annotated LATEX. We would, however, also like to extract thesemantics of statements like V = 15.2m3 (i.e. we would like to extract the fact thatthe quantity volume has a value of 15.2 in units of cubic metre). To this end we havealso added the functionality of finding binary (=, <, >, º, etc.) relations in the text tothe extraction tool.

When a PDF is parsed by the extraction tool, URIs for units and quantities, nu-meric values and binary relations are tagged in the text. Operators, like \E are alsorecognised, and in the case of exponents, the value is changed accordingly (e.g. 5.2£103 is changed to 5200). The tool then applies rules to find patterns in the text like:


If the tool comes across such a pattern, the combination of quantity, relation, value,and unit is stored. For instance the equation:

Ek = 1.209£10°2 eV (3)

is extracted as:

1 [QUANTITY=om:Kinetic_energy] [BINARY_RELATION=’=’]2 [VALUE=�.�12�9] [UNIT=om:electronvolt]

In this manner quantitative statements can be extracted from PDF generated withOM annotated LATEX.

3.5 Transformation to RDF

The result of the extraction can then be transformed into RDF statements using theOM ontology. For instance, the following equation

F = 15.2N (4)


pdflatex produces PDF with URIs as annotations★ The PDF can be parsed using a rule-based tool★ Searches for pattern:


COMMIT/ E-FOODLAB


om:unit_of_measure_


om:num

erical_value

15.2DOUBLE

mm:_15.2_NINSTANCE

mq:forceINSTANCE

om:newtonINSTANCE


om:ForceCLASS

om:MeasureCLASS

rdfs:ty

pe

om:value

rdfs:ty

pe

rdfs:ty

pe

COMMIT/ E-FOODLAB


om:unit_of_measure_


om:num

erical_value

15.2DOUBLE

mm:_15.2_NINSTANCE

mq:forceINSTANCE

om:newtonINSTANCE


om:ForceCLASS

om:MeasureCLASS

rdfs:ty

pe

om:value

rdfs:ty

pe

rdfs:ty

peFig. 1. Extracted RDF representing Equation 4. This graph only represents OM-specific data;other information such as provenance data are present in the full RDF graph.

can be transformed into RDF (in turtle format [23]):

1 mq:force om:value mm:_15.2_N;2 a om:Force .3 mm:_15.2_N a om:Measure ;4 om:numerical_value "15.2"^^xsd:double ;5 om:unit_of_measure_or_measurement_scale om:newton .

where mm and mq are prefixes for custom defined namespaces (possibly pointing tothe URI for the original text, thereby ensuring provenance) for measures and quanti-ties respectively, and om is the prefix for the OM namespace. This statement can alsobe visualised as a graph (Figure 1).

The current extraction tool is not only able to create the statements to model theequation in RDF, but it is also able to export these RDF statements to an RDF triplestore, where it can be combined with other semantic data extracted from the PDF, orobtained from other sources.

4 Real-world examples

The number of detected measures depends on the type of paper; experimental pa-pers tend to contain more measures than theoretical papers. For example the fifthpage of a paper on water vapour sorption in gluten and starch films contains thefollowing text:

[...] The obtained parameter values for starch films (T g = 540±10K and¢Cp =0.32 ± 0.02Jg°1 K°1) differ from the values obtained by van der Sman and

COMMIT/ E-FOODLAB

CONCLUSIONSOntology OM - LaTeX Annotations Conclusions

OM-LaTeX:★ Defines easy to use LaTeX commands (aliases)

★ with correct typesetting★ semantic annotations with associated concepts

(via URI links)★ Parsing of generated PDF

★ extracts equations from the PDF★ transforms into RDF

COMMIT/ E-FOODLAB

FUTURE WORKOntology OM - LaTeX Annotations Conclusions

★ More complex rules for parsing generated PDFs★ Unit conversion★ Searching★ Dimensional analysis of equations★ Connecting units and quantities with the

associated phenomena

★ Meanwhile OM will be extended even further

COMMIT/ E-FOODLAB

OM-LATEXhttp://www.wurvoc.org/vocabularies/om-1.8/

Thank you!

http://www.wurvoc

http://www.wurvoc

Technology

SWAIE presentation on the Ontology of units of Measure