Semantic Units for Scientific Data Exchange

A deceptively simple problem and a whole lot of

pedantry

Kieron Taylor – University of Southampton

Why do we need units?

Mine is bigger than yours. Yards, meters, parsecs, Angstroms – take

your pick. Convenience versus compatibility.

Computers are not psychic. Bad stuff happens if we don't use them...

Nothing wrong with my arithmetic

Gimli Glider photo originally from Soaring Magazine article by Wade H Nelson

Pounds or kilograms

Boeing 767 “lands” without fuel.

Refuelling was performed with faulty gauges. Ground crew unfamiliar with metric aircraft and calculate fuel quantity using pounds per liter (not gallons?) rather than kilograms per liter.

Whoops, there goes another satellite

Images copyright to NASA

Splat

Mars Climate Orbiter sent to Mars in 1998 before burning to a cinder in Martian atmosphere. JPL worked with Newtons, Lockheed worked with pounds. Momentum calculations off by factor of 2.2

“It's my job to follow the creative element of the band!”

“But you're not as confused as him!”

Instructing computers about units

Textual annotations insufficient. Abbreviations too ambiguous and full length descriptions are cumbersome.

Programmed capabilities in Ada, Java etc. do not transfer outside of software.

Mark-up languages allow description, but not necessarily processing.

Why is it so hard?

Multiple unit systems: SI, British Imperial, US Imperial, CGS, esu, emu.

Combinations of units are effectively limitless.

Unitless measurements, ratios. Units must imply quantities/dimensions in

order to allow comparison of combined units – W ≡ J/s ≡ m2 kg s-1

Conversions are not simple operations.

RDF and URIs

Graph network effectively describes relationships between units and quantities.

XML form can be integrated into documents.

URIs ensure documents reference the same unit definitions.

Triplestores provide a generic reasoning environment for validation and computation.

RDF Schema

Quantity

Unit

Conversion

Constant

Operator

integerpower of

derived from

has step operator

integerstep number

operation value

has SI unit

has quantity

floatvalue

integer

power of

has unitof type

stringhas symbol

string

has symbol

0.02 mol dm-3

Measurement

0.02

has-unit

has-value

has-unit

1power-of

Molunit-type

-3power-of

unit-type Meter

Deci

has-prefix

Time

Second

Force

Newton

Length

Meter

Mass

Gram

-2

derived-frompower-of

quantity-type

1power-of

quantity-type

derived-from1power-of

quantity-type

Hour

Base quantities

Derived quantities

SI Units

Non-SI Units

has-quantity

has-quantity

has-quantity

has-quantity

Pound

ConversionsFahrenheit

Temperature

Subtracthas-conversion

has-quantityhas-conversion

has-step

1

32

step-number

operator

operation-value

has-step

Divide

2

operator

1.8

rdf:value

step-number

273.15

Add

3

step-number

operator

has-step

operation-value

rdf:valueoperation-value

rdf:valuehas-unit

has-unit

Fahrenheit

type

Kelvin

type

1 -1

power-ofpower-of

Advantages of explicit conversions

Reversible processes minimises number of descriptions.

Units in conversions allow sense checking Can be generalised for another purpose:

conversions that alter the quantity as well as the value.

Physical equivalents

cm-1 = eV = nm = J

E = mc2

E = h

c = Meter

Length

Reciprocal

has-quantity

has-conversion

has-step

1step-number

operator

has-stepMultiply

2

operator

299792458

operation-value

step-number

Speed of Light

rdf:value

has-unittype

1

power-of

Secondtype

-1

power-of

has-unit

Implementation

<measurement> <value>10</value> <has-unit> <Unit rdf:type=”#Fahrenheit”> <power-of>1</power-of> </Unit> </has-unit> <has-desired-unit> <Unit rdf:type=”#Celsius”> <power-of>1</power-of> </Unit> </has-desired-unit></measurement>

<measurement> <value>-12.2</value> <has-unit> <Unit rdf:type=”#Celsius”> <power-of>1</power-of> </Unit> </has-unit></measurement>

Uniterator

Perl + Redland

Rule set“some.units-authority.org”

Outstanding issues Dimensional differences with electromagnetic

and electrostatic unit systems. Identical units/dimensions do not imply

additive quantities: Moment of force and Work are not compatible.

Arbitrary zero point scales such as celsius, and time intervals versus time points cause complications.

Restriction of conversions. When are they appropriate? Far greater software complexity is required to restrict the use of quantity-quantity conversions.

Acknowledgements

Dr. Jeremy Frey – University of Southampton

Prof. Ian Mills – Reading University Dr. Robert Gledhill – Unknown Ed Zaluska – University of Southampton