# Theory STANDARD-UNITS

This theory defines a set of basic units of measure, a set of fundamental dimensions and a few others. Each unit-of-measure is defined with its relationship to SI units for the fundamental dimensions. It is intended that this theory represent enough information to convert among any pair of units of the same dimension that are either defined as basic units here or built up from the basic units using the composition operators * and EXPT.

### Theories included by Standard-Units:

```    Physical-Quantities
Frame-Ontology
Kif-Relations
Kif-Sets
Kif-Lists
Kif-Numbers
Abstract-Algebra
Frame-Ontology ...```

### Theories that include Standard-Units:

```    Simple-Bikes
Cml
Thermodynamics
Dme
Thermodynamics
Vt-Design
Simple-Bikes
Vt-Domain
Vt-Example
Unary-Scalar-Functions
Cml ...```

### 1 class defined:

`    Si-Unit`

### 36 instances defined:

The following constants were used from included theories:

All constants that were mentioned were defined.

## Physical-dimension LENGTH-DIMENSION

The fundamental dimension of length, as defined by the SI standard.
Instance-Of: Physical-dimension

## Physical-dimension MASS-DIMENSION

The fundamental dimension of mass, as defined by the SI standard.
Instance-Of: Physical-dimension

## Physical-dimension TIME-DIMENSION

The fundamental dimension of physical, continuous time, as defined by the SI standard.
Instance-Of: Physical-dimension

## Physical-dimension ELECTRICAL-CURRENT-DIMENSION

The fundamental dimension of electrical current, as defined by the SI standard.
Instance-Of: Physical-dimension

## Physical-dimension THERMODYNAMIC-TEMPERATURE-DIMENSION

The fundamental dimension of temperature, as defined by the SI standard.
Instance-Of: Physical-dimension

## Physical-dimension AMOUNT-OF-SUBSTANCE-DIMENSION

The fundamental dimension of amount of substance, as defined by the SI standard.
Instance-Of: Physical-dimension

## Physical-dimension LUMINOUS-INTENSITY-DIMENSION

The fundamental dimension of luminous-intensity, as defined by the SI standard.
Instance-Of: Physical-dimension

## Physical-dimension FORCE-DIMENSION

The physical dimension of force is defined as mass times length over time squared. In some systems FORCE-DIMENSION is fundamental and MASS-DIMENSION is a derived dimension. This theory goes with the SI standard, but we include the definition of force as a non-fundamental built-in dimension.
Instance-Of: Physical-dimension
Axioms:
```(= Force-Dimension
(* Mass-Dimension (* Length-Dimension (Expt Time-Dimension -2))) )

```

## Physical-dimension ENERGY-DIMENSION

The physical dimension of energy is defined as mass times length squared over time squared.
Instance-Of: Physical-dimension
Axioms:
```(= Energy-Dimension
(* Mass-Dimension
(* (Expt Length-Dimension 2) (Expt Time-Dimension -2)) ))

```

## Physical-dimension CURRENCY-DIMENSION

The fundamental dimension of currency or money. CURRENCY-DIMENSION is to currencies as US-dollar's and ECU's as the LENGTH-DIMENSION is to units of length such as meters.
Instance-Of: Physical-dimension

## Class SI-UNIT

The class of Systeme International units.
Instance-Of: Class, System-of-units
Subclass-Of: Unit-of-measure
Axioms:
```(= (Base-Units Si-Unit)
(Setof Meter
Kilogram
Second-Of-Time
Ampere
Degree-Kelvin
Mole
Candela
Identity-Unit))

```

## Si-unit SECOND-OF-TIME

The SI standard unit of time. It is not called 'second' to distinguish it from the function second (from the KIF-lists ontology) that denotes the second element of a sequence.
Instance-Of: Si-unit, Unit-of-measure
Axioms:
```(= (Quantity.Dimension Second-Of-Time) Time-Dimension)

```

## Instance MINUTE

Time unit.
Axioms:
```(= Minute (* Second-Of-Time 60))

```

## Instance HOUR

Time unit.
Axioms:
```(= Hour (* Minute 60))

```

## Si-unit METER

SI length unit. No conversion function is given because this is a standard.
Instance-Of: Si-unit, Unit-of-measure
Axioms:
```(= (Quantity.Dimension Meter) Length-Dimension)

```

## Instance KILOMETER

Axioms:
```(= Kilometer (* Meter 1000))

```

## Instance INCH

English length unit.
Axioms:
```(= Inch (/ Meter 39.37))

```

## Instance FOOT

English length unit of feet.
Axioms:
```(= Foot (* Inch 12))

```

## Instance MILE

English length unit.
Axioms:
```(= Mile (* Foot 5280))

```

## Instance ANGSTROM

ang.strom 'a<nj>-str<e>m also '<o.><nj>- n (1897) [Anders J. <A^o>ngstr<o:>m]

:a unit of length equal to one ten-billionth of a meters -- used esp.

for wavelengths of light.

Axioms:
```(= Angstrom (/ Meter (Expt 10 10)))

```

## Si-unit KILOGRAM

SI mass unit of kilogram.
Instance-Of: Si-unit, Unit-of-measure
Axioms:
```(= (Quantity.Dimension Kilogram) Mass-Dimension)

```

## Instance POUND-MASS

English pound of mass.
Axioms:
```(= Pound-Mass (/ Kilogram 2.2046))

```

## Instance SLUG

English mass unit.
Axioms:
```(= Slug (/ Pound-Mass 1000))

```

## Instance NEWTON

SI force unit.
Axioms:
```(= Newton (* (* Kilogram Meter) (Expt Second-Of-Time -2)))

```

## Si-unit AMPERE

SI electrical current unit.
Instance-Of: Si-unit, Unit-of-measure
Axioms:
```(= (Quantity.Dimension Ampere) Electrical-Current-Dimension)

```

## Instance POUND-FORCE

English pound of force.
Axioms:
```(= Pound-Force (/ Newton 4.448))

```

## Instance JOULE

SI energy unit.
Axioms:
```(= Joule (* Newton Meter))

```

## Instance BTU

British thermal unit, a unit of energy.
Axioms:
```(= Btu (* 1055.0 Joule))

```

## Instance PASCAL

SI pressure unit.
Axioms:
```(= Pascal (* Newton (Expt Meter -2)))

```

## Si-unit DEGREE-KELVIN

A unit of thermodynamic temperature. The degree-Kelvin differs from the Celcius scale ...
Instance-Of: Si-unit, Unit-of-measure
Axioms:
```(= (Quantity.Dimension Degree-Kelvin)
Thermodynamic-Temperature-Dimension)

```

## Instance DEGREE-RANKINE

Being, according to, or relating to an absolute-temperature scale on which the unit of measurement equals a Fahrenheit degree and on which the freezing point of water is 491.67<^o> and the boiling point 671.67<^o>. [Webster]
Axioms:
```(= Degree-Rankine (* Degree-Kelvin (/ 5 9)))

```

Angular measurement unit.
Axioms:
```(= Radian Identity-Unit)

```

## Instance DEGREE

Angular measurement unit.
Axioms:
```(= Degree (* Radian (/ Pi 180)))

```

## Unit-of-measure US-DOLLAR

An example currency unit.
Instance-Of: Unit-of-measure
Axioms:
```(= (Quantity.Dimension Us-Dollar) Currency-Dimension)

```

## Instance US-CENT

Currency measurement unit.
Axioms:
```(= Us-Cent (/ Us-Dollar 100))

```

## Si-unit MOLE

SI unit for amount of substance. A mole of a substance is the amount of that substance that contains 6.02252 x 10^23 elementary entities. Those entities may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. One mole of carbon atoms (the C^12 isotope) is exactly 12 grams [Halliday and Resnick]. In this ontology we say that the specified unit is the molecule, so that the MOLE stands by itself as a unit.
Instance-Of: Si-unit, Unit-of-measure
Axioms:
```(= (Quantity.Dimension Mole) Amount-Of-Substance-Dimension)

```

## Si-unit CANDELA

The CANDELA is the SI unit for luminous intensity.
Instance-Of: Si-unit, Unit-of-measure
Axioms:
```(= (Quantity.Dimension Candela) Luminous-Intensity-Dimension)

```

This document was generated using Ontolingua.
Formatting and translation code was written by
François Gerbaux and Tom Gruber