1. QUDT An OWL Ontology for Quantities, Units, Dimensions and Data Types Han Wang April 3 rd, 2013

2. Introduction Developed by TopQuadrant and NASA for NASA Exploration Initiatives Ontology Models (NExIOM) project. A unified model of physical quantities, units of measure, and their dimensions in various measurement systems. 4/3/131

3. Classes 4/3/132 http://qudt.org/

4. Classes – cont’d Quantity –An observable property of an object, event or system that can be measured and quantified numerically. –Differentiated by two attributes: quantityKind and quantityValue. –If two quantities are of the same kind, their magnitudes (values) can be compared and ordered. 4/3/133

5. Classes – cont’d QuantityKind –Any observable property that can be measured and quantified numerically. –E.g. length, mass, currency, interest rate, etc. QuantityValue –The numerical value of a quantity with respect to a chosen unit of measure. 4/3/134

6. Classes – cont’d Unit –A particular quantity of a given kind that has been chosen as a scale for measuring other quantities of the same kind. 4/3/135

7. Classes – cont’d SystemOfQuantities –A set of one or more quantity kinds together with a set of zero or more algebraic equations that define relationships between quantity kinds in the set. –E.g. SI system, CGS system –Base quantity kinds (e.g. length, mass, time) –Derived quantity kinds (e.g. area, force, power) 4/3/136

8. Classes – cont’d SystemOfUnits –A set of units which are chosen as the reference scales for some set of quantity kinds together with the definitions of each unit. –Base units (e.g. meter, kilogram, second) –Derived units (e.g. square meter, newton, watt) 4/3/137

9. Classes – cont’d Dimension –a mapping from a tuple of rational numbers to a product of base quantity kinds such that the tuple members correspond to the exponents of the base quantity kinds. –E.g. A = L 2, F = L 1 M 1 T -2, P = L 2 M 1 T -3 –dim Q = (B1) d1 (B2) d2 …(Bn) dn 4/3/138

10. Examples Value of Planck’s Constant in SI and CGS Units 4/3/139

11. Examples – cont’d Dimensions for Permittivity 4/3/1310

12. Applications: SPIN Functions Unit conversion 4/3/1311

13. Applications: SPIN Functions – cont’d Unit conversion 4/3/1312

14. Conclusion A straightforward model for representing physical quantities. Capable of rule-based inference. Not so much on metadata of the quantities. 4/3/1313

15. References http://qudt.org/ http://ontolog.cim3.net/file/work/UoM/ UoM-standard- ontology_20090924/QUDT-overview-- JamesMasters_20090924.pdfhttp://ontolog.cim3.net/file/work/UoM/ UoM-standard- ontology_20090924/QUDT-overview-- JamesMasters_20090924.pdf http://linkedmodel.org/catalog/qudt/1. 1/http://linkedmodel.org/catalog/qudt/1. 1/ 4/3/1314