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SWAIE presentation on the Ontology of units of Measure

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When using units and quantities in equations or in text, ambiguity in the use of symbols may exist, especially if a (quantitative) text is read by someone who is not an expert in the field. Symbols …

When using units and quantities in equations or in text, ambiguity in the use of symbols may exist, especially if a (quantitative) text is read by someone who is not an expert in the field. Symbols for one quantity or unit used in one field of research may overlap symbols used in other fields of research. The Ontology of units of Measure (OM) aims to disambiguate the use of quantitative information in text. This presentation shows how semi-automatic annotation of text can be used with OM to disambiguate quantitative information not only in text but also in other formats such as excel sheets.

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  • 1. OM-L ATEXIDENTIFYING AND EXTRACTING QUANTITATIVE DATA IN ANNOTATED TEXTDon Willems, Hajo Rijgersberg, and Jan Top COMMIT/ E-FOODLAB
  • 2. UNITS and QUANTITIESUnit of measurement ★ a definite magnitude of a ‘physical’ quantity ★ used as a standard Length (l) metre (m) COMMIT/ E-FOODLAB
  • 3. UNITS and QUANTITIESUnit of measurement ★ a definite magnitude of a ‘physical’ quantity ★ used as a standard ★ used for the measurement of the same quantity COMMIT/ E-FOODLAB
  • 4. UNITS and QUANTITIESUnit of measurement ★ a definite magnitude of a ‘physical’ quantity ★ used as a standard ★ used for the measurement of the same quantity l = 0.589 x 1m l = 0.091 x 1m COMMIT/ E-FOODLAB
  • 5. UNITS and QUANTITIESUnit of measurement ★ a definite magnitude of a ‘physical’ quantity ★ used as a standard ★ used for the measurement of the same quantity l = 58.9 cm l = 9.1 cm COMMIT/ E-FOODLAB
  • 6. UNITS and QUANTITIESUnit of measurement ★ a definite magnitude of a ‘physical’ quantity ★ used as a standard ★ used for the measurement of the same quantity l = 1.93 ft l = 3.6 in COMMIT/ E-FOODLAB
  • 7. UNITS and QUANTITIESUnit of measurement ★ a definite magnitude of a ‘physical’ quantity ★ used as a standard ★ used for the measurement of the same quantity l= 1.91x10 -17 pc l = 9.1x108 Å COMMIT/ E-FOODLAB
  • 8. AMBIGUITY Second COMMIT/ E-FOODLAB
  • 9. AMBIGUITY 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 Second COMMIT/ E-FOODLAB
  • 10. AMBIGUITY 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 Second Second of arc (’’) 1/3600 of 1° or 8/100.000.000 of a full circle COMMIT/ E-FOODLAB
  • 11. AMBIGUITY 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 Sidereal second (s) Second 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 COMMIT/ E-FOODLAB
  • 12. AMBIGUITY M COMMIT/ E-FOODLAB
  • 13. AMBIGUITY Mutual Inductance Moment of Force Quantum number of component of J in the direction of an external fieldMagnetisation M Molar MassAbsolute Magnitude Luminous Exitance Magnetic Quantum Radiant Exitance Number COMMIT/ E-FOODLAB
  • 14. GOAL Disambiguation of Units and Quantities Easy Annotation in LATEXCorrect Formatting of Units and Quantities COMMIT/ E-FOODLAB
  • 15. OUTLINE OntologyOM - LATEXAnnotationsConclusions COMMIT/ E-FOODLAB
  • 16. ONTOLOGY of UNITS of MEASURE Ontology OM - LaTeX Annotations ConclusionsThe 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: COMMIT/ E-FOODLAB
  • 17. ONTOLOGY of UNITS of MEASURE - sources Ontology 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 COMMIT/ E-FOODLAB
  • 18. ONTOLOGY of UNITS of MEASURE - structure Ontology OM - LaTeX Annotations Conclusions Prefix System of units CLASS CLASS de t ba r iv ni t se ed eu ni prefix s u q ua qu ba an ived nt it tit d er y y definition Unit of measure Quantity CLASS unit of measure CLASS l e dimension ca measure un unit of it ts of m en ea r em su re a su e Measure m CLASS Measurement scale Dimension numerical value (Float) CLASS CLASS COMMIT/ E-FOODLAB
  • 19. ONTOLOGY of UNITS of MEASURE - structure Ontology OM - LaTeX Annotations Conclusions om:Force om:Measure om:Singular_unit CLASS CLASS CLASS rdfs:type rdfs:type mq:force om:value mm:_15.2_N INSTANCE INSTANCE rdfs:type o om:numerical_value or m:u _m n ea it_o su f_ re me m a en su t_ re sc _ ale 15.2 om:newton DOUBLE INSTANCE COMMIT/ E-FOODLAB
  • 20. ONTOLOGY of UNITS of MEASURE - comparisson Ontology OM - LaTeX Annotations Conclusions OntologyConcept or relation EngMath SUMO ScadaOnWeb SWEET Unit OpenMath OMUnit of Measure ✔ ✔ ✔ ✔ ✔Prefix ✔ ✔ ✔ ✔Quantity ✔ ✔ ✔ ✔Measurement Scale ✔ ✔Measure ✔ ✔System of Units ✔ ✔Dimension ✔ ✔ ✔ ✔Quantities formally refer to units ✔ ✔ ✔ ✔ ✔Units of measure have formaldefinitions in terms of other units ✔ ✔ ✔ ✔ ✔ ✔Multiples and submultiples of unitsrefer to predefined prefixes ✔ ✔ ✔ COMMIT/ E-FOODLAB
  • 21. ONTOLOGY of UNITS of MEASURE - applications Ontology 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 COMMIT/ E-FOODLAB
  • 22. ONTOLOGY of UNITS of MEASURE - applications Ontology OM - LaTeX Annotations Conclusions COMMIT/ E-FOODLAB
  • 23. ONTOLOGY of UNITS of MEASURE - applications Ontology OM - LaTeX Annotations Conclusions COMMIT/ E-FOODLAB
  • 24. ONTOLOGY of UNITS of MEASURE - applications Ontology OM - LaTeX Annotations Conclusions COMMIT/ E-FOODLAB
  • 25. OM-LATEX Ontology OM - LaTeX Annotations ConclusionsLaTeX ★ 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 COMMIT/ E-FOODLAB
  • 26. ad of retyping these command structu OM-LATEX code becomes more difficult source Ontology OM - LaTeX Annotations Conclusionsn. To create a statement like: °11 2 °2 G = 6.673 £ 10 N m kgnal constant, the following LTEX sourc A G = 6.673times 10^{-11} mathrm{N} mathrm{m^2} mathrm{kg^{-2}} g/vocabularies/om-1.8/. The objective ociated web services relevant to the generaparticular the domains of life sciences and COMMIT/ E-FOODLAB
  • 27. OM-LATEX Ontology OM - LaTeX Annotations Conclusionsnewcommand{Gunit}{mathrm{N} mathrm{m^2} mathrm{kg^{-2}}}newcommand{E}[1]{times10^{#1}} COMMIT/ E-FOODLAB
  • 28. ad of retyping these command structu OM-LATEX code becomes more difficult source Ontology OM - LaTeX Annotations Conclusionsn. To create a statement like: °11 2 °2 G = 6.673 £ 10 N m kgnal constant, the following LTEX sourc A G = 6.673times 10^{-11} mathrm{N} mathrm{m^2} mathrm{kg^{-2}} g/vocabularies/om-1.8/. The objective ociated web services relevant to the generaparticular the domains of life sciences and COMMIT/ E-FOODLAB
  • 29. ad of retyping these command structu OM-LATEX code becomes more difficult source Ontology OM - LaTeX Annotations Conclusionsn. To create a statement like: °11 2 °2 G = 6.673 £ 10 N m kgnal constant, the following LTEX sourc A G = 6.673E{-11} GUnit g/vocabularies/om-1.8/. The objective ociated web services relevant to the generaparticular the domains of life sciences and COMMIT/ E-FOODLAB
  • 30. 16= 170 typesetting OM-LATEX - K is 2.987 £ 10 = the temperature 2 °20 °3 2410 Ontology kg = 5.163 £(uniform m is the 10 £ 4 OM - LaTeX Annotations Conclusions 34 = 2.3 £ 10 kg µ 3.1416 £ 1.3 4 MJ = 1.2 £ 10 MØ = °27 kg 3.7 £ 10 ° ¢3 16 2 = 2.987 £ 10cloud is supported only COMMIT/ E-FOODLAB
  • 31. 16= 170 typesetting OM-LATEX - K is 2.987 £ 10 = the temperature 2 °20 °3 2410 Ontology kg = 5.163 £(uniform m is the 10 £ 4 OM - LaTeX Annotations Conclusions 34 2.3 £ 10 kg Quantities: Italics = µ Subscripts are not in italics except when they refer to 3.1416 £ 1.3 another quantity 4 MJ = 1.2 £ 10 MØ = °27 kg 3.7 £ 10 ° ¢3 16 2 = 2.987 £ 10cloud is supported only COMMIT/ E-FOODLAB
  • 32. 16= 170 typesetting OM-LATEX - K is 2.987 £ 10 = the temperature 2 °20 °3 2410 Ontology kg = 5.163 £(uniform m is the 10 £ 4 OM - LaTeX Annotations Conclusions 34 2.3 £ 10 kg Quantities: Italics = µ Subscripts are not in italics except when they refer to 3.1416 £ 1.3 another quantity 4 MJ = 1.2 £ 10 MØ = °27 kg 3.7 £ 10 Units: No italics ° ¢3 16 2 = 2.987 £ 10cloud is supported only COMMIT/ E-FOODLAB
  • 33. OM-LATEX - package Ontology OM - LaTeX magnetomo Annotations ConclusionsOM-LaTeX Magnetomotiv ★ Generated automatically from the Ontology ★ Includes hyperlinks with the relevant URI ★ Defines commands for units and quantities in OM ★ om:metre becomes metre potential) to th ★ om:Molar_heat_capacity becomes MolarHeatCapacity Symbol: F m ★ Includes correct typesetting ★ MagnetomotiveForce becomes COMMIT/ E-FOODLAB
  • 34. °20 - package°3 2410 OM-L kg = 5.163 £ 10 £ 4. ATEX Ontology m is the (uniform OM - LaTeX Annotations Conclusions 34 = 2.3 £ 10 kg µ 3.1416 £ 1.3 4 MJ = 1.2 £ 10 MØ = °27 kg £ 3.7 £ 10 ° ¢3 16 2 = 2.987 £ 10cloud is supported 24 only = 5.163 £ 10 E-FOODLAB4 COMMIT/ £
  • 35. °20 - package°3 2410 OM-L kg = 5.163 £ 10 £ 4. ATEX Ontology m is the (uniform OM - LaTeX Annotations Conclusions 34 2.3 £ 10 kg µ = 3.1416 £ 1.3 4 M J = 1.2 £ 10 MØ = °27 kg £ 3.7 £ 10 ° ¢2 JeansMass = 1.2E{4} solarMass 3 16 = 2.987 £ 10cloud is supported 24 only = 5.163 £ 10 E-FOODLAB4 COMMIT/ £
  • 36. 16= 170 annotations OM-LATEX - K is 2.987 £ 10 = the temperature 2 °20 °3 2410 Ontology kg = 5.163 £(uniform m is the 10 £ 4 OM - LaTeX Annotations Conclusions 34 = 2.3 £ 10 kg µ 3.1416 £ 1.3 4 MJ = 1.2 £ 10 MØ = °27 kg 3.7 £ 10 ° ¢3 16 2 = 2.987 £ 10cloud is supported only COMMIT/ E-FOODLAB
  • 37. 16= 170 annotations OM-LATEX - K is 2.987 £ 10 = the temperature 2 °20 °3 2410 Ontology kg = 5.163 £(uniform m is the 10 £ 4 OM - LaTeX Annotations Conclusions 34 = 2.3 £ 10 kg µ om:Jeans_mass 3.1416 £ 1.3 4 MJ = 1.2 £ 10 MØ = °27 kg 3.7 £ 10 om:solar_mass ° ¢3 16 2 = 2.987 £ 10cloud is supported only COMMIT/ E-FOODLAB
  • 38. OM-LATEX - package Ontology OM - LaTeX Annotations ConclusionsEach command has an optional parameter ★ Without parameter in math mode: ★ RelativePressureCoefficient results in: p p ÆÆ ★ With parameter in math mode: p ★ RelativePressureCoefficient[c_p] results in: p c c Æp ★ With parameter in text mode: cp coefficien coefficie ★ RelativePressureCoefficient[coefficient] results in: coefficient ★ All annotated with the same URI COMMIT/ E-FOODLAB
  • 39. OM-LATEX - package Ontology OM - LaTeX Annotations ConclusionsEach command has an optional parameter ★ Without parameter in math mode: ★ RelativePressureCoefficient results in: p p ÆÆ ★ With parameter in math mode: p ★ RelativePressureCoefficient[c_p] results in: p c c Æp ★ With parameter in text mode: cp ★ RelativePressureCoefficient[coefficient] results in: coefficien coefficie coefficient ★ All annotated with the same URI om:Relative_pressure_coefficient COMMIT/ E-FOODLAB
  • 40. OM-LATEX - comparison with SIUnits Ontology OM - LaTeX Annotations Conclusions LaTeX Package SIUnits OM-LaTeXSI 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. kilometrepersecond COMMIT/ E-FOODLAB
  • 41. ANNOTATIONS Ontology OM - LaTeX Annotations ConclusionsAnnotations: ★ 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
  • 42. ANNOTATIONS - parsingn then be transformed i Ontology OM - LaTeX Annotations Conclusions pdflatex produces PDF with URIs as annotationse following equation ★ ★ The PDF can be parsed using a rule-based tool Searches for pattern: [QUANTITY] [BINARY_RELATION] [VALUE] [UNIT] F = 15.2 N COMMIT/ E-FOODLAB
  • 43. ANNOTATIONS - parsingn then be transformed i Ontology OM - LaTeX Annotations Conclusions pdflatex produces PDF with URIs as annotationse following equation ★ ★ The PDF can be parsed using a rule-based tool Searches for pattern: [QUANTITY] [BINARY_RELATION] [VALUE] [UNIT] F = 15.2 N QUANTITY BINARY RELATION VALUE UNIT COMMIT/ E-FOODLAB
  • 44. ANNOTATIONS - parsing Ontology OM - LaTeX Annotations Conclusions om:Force om:Measure om:Singular_unit CLASS CLASS CLASS rdfs:type rdfs:type mq:force om:value mm:_15.2_N INSTANCE INSTANCE rdfs:type o om:numerical_value or m:u _m n ea it_o su f_ re me m a en su t_ re sc _ ale 15.2 om:newton DOUBLE INSTANCE COMMIT/ E-FOODLAB
  • 45. DOUBLE INSTANCE ANNOTATIONS - parsingExtracted RDF representing Equation 4. This graph only represents OM-specificnformation such as provenance data are present in the full RDF graph. Ontology OM - LaTeX Annotations Conclusionse transformed into RDF (in turtle format [23]): mq:force om:value mm:_15.2_N; a om:Force . mm:_15.2_N a om:Measure ; om:numerical_value "15.2"^^xsd:double ; om:unit_of_measure_or_measurement_scale om:newton .e mm and mq are prefixes for custom defined namespaces (possibly pointiRI for the original text, thereby ensuring provenance) for measures and qu spectively, and om is the prefix for the OM namespace. This statement can ualised as a graph (Figure 1).he current extraction tool is not only able to create the statements to mod COMMIT/ E-FOODLAB ion in RDF, but it is also able to export these RDF statements to an RDF
  • 46. CONCLUSIONS Ontology OM - LaTeX Annotations ConclusionsOM-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
  • 47. FUTURE WORK Ontology 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
  • 48. OM-L ATEXhttp://www.wurvoc.org/vocabularies/om-1.8/ Thank you! COMMIT/ E-FOODLAB