What XML Schema Designers Need to Know About Measurement Units

1
What XML Schema Designers Need to Know About
Measurement Units

• Frank Olken and John McCarthy
• Lawrence Berkeley National Laboratory
• Presented to XTECH 2000, San Jose, CA
• February 29, 2000

2
Content of Talk

• Syntax issues - markup
• Semantics- units, dimensionality
• Architecture - references to shared registries
• Units registry operations - who???

3
What is the issue?

• XML is used for data exchange
• Often used to encode measured quantities
• e.g., for Ecommerce, engineering, medicine
• How do we encode measurement units?

4
Why do we need measurement units?

• Quantities without units are meaningless !!!
• Misunderstandings about units causes
• loss of spacecraft (Mars Climate Explorer)
• contractual disputes
• potential loss of life (in medicine)
• Common error
• Delusions of shared assumptions about measurement
  units.

5
Actually two issues

• What do we need to specify?
• Units
• Dimensionality
• Property ?
• How do we write it in XML?

6
XML encodings of units

• Implicitly structured strings
• ltheightgt 5 inches lt/heightgt
• bad style (requires special parser)

7
XML encodings of units

• Explicit markup is better, e.g.,
• ltspeedgt
• ltvaluegt 5 lt/valuegt
• ltunitsgt km/hr lt/unitsgt
• lt/speedgt
• advantage easy to identify units info.
• problem parsing units values still requires
  special purpose parser

8
XML encodings of units

• Explicit markup with namespaces/URIs
• ltx xmlnsisoUnitshttp//www.iso.org/units gt
• ltspeedgt
• ltvaluegt 5 lt/valuegt
• ltunitsgt ltxlink typesimple, REFisoUnitskmPer
  Hour /gt lt/unitsgt
• lt/speedgt lt/xgt
• advantages
• exploits existing lookup mechanism
• standard units designators, mechanism for
  checking dimensional consistency
• disadvantage
• nonstandard units names (XML prohibits slashes
  in IDs)

9
Architecture of XML Units Encoding

• Use URI references from schemas/instances into
  standard units registries
• Units/Dimensionality registries have detailed
  fully marked up descriptions of derived/composite
  units/dimensions in terms of
• Basis units/dimensions

10
Basis units declaration (XML)

• ltunitdecl ID"meter" /gt
• ltnamegt meter lt/namegt
• ltUnitTypegt Base lt/UnitTypegt
• ltsymbolgt m lt/symbolgt
• ltdimensionalitygt ltA
  xmllinksimple REFlength" /gt
• lt/dimensionalitygt
• ltdefinitiongt
• Length of path traveled
  by light in a time interval of
• 1/299,792,458 second.
• lt/definitiongt
• ltcitegt ltA xmllinksimple ref..
  /gt lt/citegt
• lt/unitdeclgt

11
Derived units declaration (XML)

• ltunitdecl ID"inch" /gt
• ltnamegt Inch lt/namegt
• ltsymbol gt in lt/symbolgt
• ltunitTypegt Derived lt/unitTypegt
• ltdimensionalitygt ltA
  xmllinksimple REF"length" /gt
• lt/dimensionalitygt
• ltconversionfactorgt 0.0254
  lt/conversionfactorgt
• ltunits REF"meter" /gt
• lt/unitdeclgt

12
Composite units decl. (XML)

• ltunitdecl ID"metersPerSecond" gt
• ltnamegt MetersPerSecond lt/namegt ltUnitTypegt
  Composite lt/UnitTypegt
• ltdimensionalitygt ltA xmllinksimple
  REF"DimSpeed" /gt
• lt/dimensionalitygt
• ltunitsgt
• ltnumeratorgt
• ltunitgt ltradixgt ltA xmllink"simple"
  REF"meter" /gtlt/radixgt
• ltexponentgt 1 lt/exponentgt
  lt/unitgtlt/numeratorgt
• ltdenominatorgt
• ltunitgt ltradixgt ltA xmllink"simple"
  REF"second"/gtlt/radixgt
• ltexponentgt 1
  lt/exponentgt lt/unitgt ltdenominatorgt
• lt/unitsgt
• lt/unitdeclgt

13
Units vs. Dimensionality

• Units
• representational issue
• e.g., feet, meters, centimeters
• Dimensionality
• semantic concept
• e.g., mass, length, time
• speed length / time

14
Units not sufficient, need dimensionality

• Example tons
• unit of mass
• unit of power (refrigeration)
• unit of energy (megatons)
• These are all homonyms which need to be
  distinguished, hence
• Also need to specify dimensionality

15
Dimensional consistency

• Units with same dimensionality are said to be
  dimensionally consistent
• Examples
• Dimensionality time
• units seconds, minutes, hours, days
• Dimensionality length
• units feet, inches, meters, kilometers
• Dimensionality Length / Time
• units kilometers / hour, meters/second,
  miles/hour

16
Significance of dimensional consistency

• Usually IMPLIES
• Comparability
• Additivity
• Automated unit conversion
• Some exceptions to these rules
• (see below)

17
Classic representation of dimensionality

• Product of powers of basis dimensions
• Basis dimensions
• mass, length, time, number of (moles), current,
  luminous intensity, temperature
• Exponents
• integers, range from -4 to 4
• Example
• energy Mass Length2 Time(-2)

18
Dimensionless quantities concentration

• mass/mass, moles/moles, or volume/volume
• Classic theory says these are dimensionally
  consistent, hence comparable, additive .
• NO !!!
• Need to distinguish dimensionless mass, molar,
  volumetric ratios

19
Revised dimensionality

• Numerator
• product of non-negative powers of basis
  dimensions
• Denominator
• product of non-negative powers of basis
  dimensions
• Can distinguish
• mass/mass vs. moles / moles
• Problem breaks the dimensional algebra

20
When to specify units/dimensionality?

• Specify in schema? Or in instance?
• Preferred
• specify both dimensionality and units in schema
• homogeneous units in document instance produces
  fewer errors
• easier to search

21
Second best choice

• Specify dimensionality in schema
• Specify units in document instance
• e.g., per element instance
• e.g, dimensionality length (in schema)
• Units feet or meters (in instance)
• Advantage can check for plausible units

22
Worst Choice

• Specify both units and dimensionality in document
  instances.
• Checking of dimensions is impossible.
• Can check for units consistent with
  dimensionality.
• Necessary for heterogeneous catalogs ...

23
Ideal XML Encoding of Units and Dimensionalities

• Extend XML Schema Basic Datatypes
• Add facets on types to encode units and
  dimensionality
• Hence, schema/query processor can check units and
  dimensionality
• Problems huge type lattice, complex type
  checking / unit conversion

24
XML Encoding Considerations

• Use detailed markup to specify units and
  dimensionality.
• This simplifies design of processor for checking
  units compatibility and automatic units
  conversion.
• Result is very verbose - see above.

25
Practical XML Encoding Solution

• Store detailed units/dimensionality info at well
  known site
• Use URI reference to point to full
  units/dimensionality specification
• Use namespaces to shorten URI reference in
  instances
• Need canonical encodings of units for URI
  references

26
Corollaries

• Someone needs to maintain units/dimensionality
  repositories
• Separate applications to check units
  compatibility are needed
• Can automate units conversion
• Implies standard XML query language will not
  check units .

27
Basis Dimension Declaration (XML)

• ltdimensiondecl ID"length" gt
• ltnamegt length lt/namegt
• ltDimensionTypegt Base
  lt/DimensionTypegt
• ltdefinitiongt
• A measurement of
  distance.
• lt/definitiongt
• ltcitegt ltA xmllink"simple"
  REF"...." /gt lt/citegt
• ltexampleUnitsgt
• Meters, ....
• lt/exampleUnitsgt
• lt/dimensiondeclgt

28
Composite Dimensionality Declaration (XML)

• ltdimensiondecl ID"DimSpeed" gt
• ltnamegt Speed lt/namegt
• ltDimensionTypegt Composite lt/DimensionTypegt
• ltdimensionalitygt
• ltnumeratorgt ltdimensiongt
• ltradixgt ltA xmllink"simple"
  REF"length" /gt lt/radixgt
• ltexponentgt 1 lt/exponentgt
  lt/dimensiongt lt/numeratorgt
• ltdenominatorgtltdimensiongt
• ltradixgt lt XLINK REF"time" gt
  lt/radixgt
• ltexponentgt 1 lt/exponentgt
  lt/dimensiongt ltdenominatorgt
• lt/dimensionalitygt
• lt/dimensiondeclgt

29
Who will maintain the XML units repository?

• W3C ? No, lacks units expertise
• OASIS? (xml.org) ?
• Intl. Scientific Societies IUPAC? ICSU?
• NIST ?
• Engineering Societies IEEE ? ASME?
• ASTM ?
• American Physics Society? American Chemical
  Society ?
• UN/CEFACT ? (ebXML.org)?
• ISO? IEC ?

30
Measures vs. Coordinates

• Measures
• length
• temperature difference
• time
• subtended angle

• Coordinates
• position
• absolute temperature
• datetimestamp
• latitude/longitude

31
Automatic unit conversion

• Only for dimensionally consistent units
• Convert to/from canonical (SI) units
• hence O(n) conversion factors, vs. O(n2)
  converson factors

32
Dimensionally inconsistent unit conversions

• Example mass to/from volume
• wheat in bushels or in tons
• oil in barrels or tons
• Very common in commerce
• Requires knowledge of material density
• Should be done explicitly (user/application)

33
Additional complexities

• Dimensionality is not sufficient to specify type
  lattice
• Example
• torque and work (energy)
• same dimensionality
• Mass Length2 / Time2
• but these are incommensurate
• torque cross product, work dot product

34
Implications

• Need to subtype dimensionality to differing
  properties
• May need rules on comparability, additivity of
  properties (subtypes) of common dimensionality

35
Conclusions

• Must specify both units and dimensionality
• either in schema or instances
• Use product of basis dimensions (units)
• Use URI references to detailed specs
• Dimensional analysis theory is incomplete
• Custodian organization for units repository?

36
Acknowledgements

• This work supported by U.S. Environmental
  Protection Agency, Superfund Office
• Program manager Bruce Bargmeyer
• Also thank Peter Murray-Rust, Malcolm Panthaki,
  Max Sherman, for discussions, suggestions, etc.

37
Contact Information

• Frank Olken, olken_at_lbl.gov, http//pueblo.lbl.gov/
  olken Lawrence Berkeley National Lab, Mailstop
  50B-3238, 1 Cyclotron Road, Berkeley, CA
  94720, Tel [phone]
  Pager 510-442-7361
• John L. McCarthy, jlmccarthy_at_lbl.gov,
  http//www.lbl.gov/mccarthy Lawrence Berkeley
  National Lab, Mailstop 50C, 1 Cyclotron Road,
  Berkeley, CA 94720, Tel [phone]

38
Bibliography

• Olken, F., McCarthy,J. Measurement Units in XML
  Datatypes, http//www.lbl.gov/olken/mendel/w3c/x
  ml.schema.wg/units/ syntax.htm , June 1999
• Olken, F., McCarthy,J. Simplified Measurement
  Units for XML Datatypes, http//www.lbl.gov/olke
  n/mendel/w3c/xml.schema.wg/units/
  simplesyntax.htm , June 1999
• Hart, George W. Multidimensional analysis
  algebras and systems for science and engineering
  /, George W. Hart. New York Springer-Verlag,
  c1995.
• Schadow, G McDonald, CJ Suico, JG Föhring, U
  Tolxdorff, T. "Units of measure in clinical
  information systems", Journal of the American
  Medical Informatics Association, 1999 Mar-Apr,
  vol. 6 number 2, pages151-62.

39
Bibliography (cont.)

• Taylor, Barry. Guide for the Use of the
  International System of Units (SI) NIST Special
  Publication 811, 1995 Edition, U.S. National
  Institute of Standards and Technology
• ISO TC-12. ISO 311992 Parts 0-13 Quantities and
  units, ISO Standards Handbook, International
  Organization for Standardization, 345 pages, 3rd
  edition, Geneva, 1993, ISBN 92-67-10185-4.
  (Available in the United States from ANSI)
  (Contains multiple ISO standards )
• .Gruber, T.R. Olsen, G.R. An ontology for
  engineering math-ematics. in (Edited by Doyle,
  J. Sandewall, E. Torasso, P.) Proc, of 4th
  International Conference on Principles of
  Knowledge Representation and Reasoning (KR'94),
  Bonn, Germany, 24-27 May 1994.) San Francisco,
  CA, USA Morgan Kaufmann Publishers, 1994.
  p.258-69 (See also URL http//www-ksl.stanfor
  d.edu /knowledge-sharing/papers/engmath.html )

40
Bibliography (cont.)

• Monica Gayle Funston, Walter Gerstle, and Malcolm
  Panthaki, "Quantity, Revisited An
  Object-Oriented Reusable Class", URL
  http//www.arc.unm.edu/CoMeT/publication/quantity.
  html, 1998(?)
• Greene, Stephan. Metadata for units of measure
  in social science databases, International
  Journal of Digital Libraries, (1977), vol. 1, pg.
  161-175
• de Boer, J. On the Hisotry of Quantity
  Calculus, Metrologia, 1994/1995, vol. 32, pg.
  405-429
• Gehani, Narain H. Databases and Units of
  Measure, IEEE. Tans. On Software Engineering,
  vol. SE-8, no. 6, Nov. 1982, pg. 605-611.
• Karr, M. and Loveman, D.B. Incoporation of
  Units into Programming Languages, Comm. ACM, May
  1978, vol. 21, no. 5, pg. 385-390
• many, many other papers/standards . Send
  citations to olken_at_lbl.gov I will post to my
  web site.