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.

**Source code: standard-units.lisp****List of other known theories**

Physical-QuantitiesFrame-OntologyKif-RelationsKif-SetsKif-ListsKif-NumbersAbstract-AlgebraFrame-Ontology...

Simple-BikesCmlThermodynamicsDmeThermodynamicsVt-DesignSimple-BikesVt-DomainVt-ExampleUnary-Scalar-FunctionsCml...

Si-Unit

**Amount-Of-Substance-Dimension****Ampere****Angstrom****Btu****Candela****Currency-Dimension****Degree****Degree-Kelvin****Degree-Rankine****Electrical-Current-Dimension****Energy-Dimension****Foot****Force-Dimension****Hour****Inch****Joule****Kilogram****Kilometer****Length-Dimension****Luminous-Intensity-Dimension****Mass-Dimension****Meter****Mile****Minute****Mole****Newton****Pascal****Pound-Force****Pound-Mass****Radian****Second-Of-Time****Slug****Thermodynamic-Temperature-Dimension****Time-Dimension****Us-Cent****Us-Dollar**

**The following constants were used from included theories:**

******defined as a***function***in theory***Kif-Numbers********defined as a***function***in theory***Physical-Quantities****/***defined as a***function***in theory***Kif-Numbers****/***defined as a***function***in theory***Physical-Quantities****Base-Units***defined as a***function***in theory***Physical-Quantities****Class***defined as a***class***in theory***Frame-Ontology****Documentation***defined as a***relation***in theory***Frame-Ontology****Expt***defined as a***function***in theory***Kif-Numbers****Expt***defined as a***function***in theory***Physical-Quantities****Identity-Dimension***defined as a***object***in theory***Physical-Quantities****Identity-Unit***defined as a***object***in theory***Physical-Quantities****Physical-Dimension***defined as a***class***in theory***Physical-Quantities****Pi***defined as a***object***in theory***Kif-Numbers****Quantity.Dimension***defined as a***function***in theory***Physical-Quantities****Subclass-Of***defined as a***relation***in theory***Frame-Ontology****System-Of-Units***defined as a***class***in theory***Physical-Quantities****Unit-Of-Measure***defined as a***class***in theory***Physical-Quantities**

**All constants that were mentioned were defined.**

The fundamental dimension of length, as defined by the SI standard.

**Instance-Of:**Physical-dimension

**Defined in theory: Standard-units****Source code: standard-units.lisp**

The fundamental dimension of mass, as defined by the SI standard.

**Instance-Of:**Physical-dimension

**Defined in theory: Standard-units****Source code: standard-units.lisp**

The fundamental dimension of physical, continuous time, as defined by the SI standard.

**Instance-Of:**Physical-dimension

**Defined in theory: Standard-units****Source code: standard-units.lisp****Also defined in:**Thermodynamics

The fundamental dimension of electrical current, as defined by the SI standard.

**Instance-Of:**Physical-dimension

**Defined in theory: Standard-units****Source code: standard-units.lisp**

The fundamental dimension of temperature, as defined by the SI standard.

**Instance-Of:**Physical-dimension

**Defined in theory: Standard-units****Source code: standard-units.lisp**

The fundamental dimension of amount of substance, as defined by the SI standard.

**Instance-Of:**Physical-dimension

**Defined in theory: Standard-units****Source code: standard-units.lisp**

The fundamental dimension of luminous-intensity, as defined by the SI standard.

**Instance-Of:**Physical-dimension

**Defined in theory: Standard-units****Source code: standard-units.lisp**

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))) )

**Defined in theory: Standard-units****Source code: standard-units.lisp**

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)) ))

**Defined in theory: Standard-units****Source code: standard-units.lisp**

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

**Defined in theory: Standard-units****Source code: standard-units.lisp**

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))

**Defined in theory: Standard-units****Source code: standard-units.lisp**

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)

**Defined in theory: Standard-units****Source code: standard-units.lisp**

Time unit.

**Axioms:**

(= Minute (* Second-Of-Time 60))

**Defined in theory: Standard-units****Source code: standard-units.lisp****Also defined in:**Jat-generic

Time unit.

**Axioms:**

(= Hour (* Minute 60))

**Defined in theory: Standard-units****Source code: standard-units.lisp****Also defined in:**Jat-generic

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)

**Defined in theory: Standard-units****Source code: standard-units.lisp**

**Axioms:**

(= Kilometer (* Meter 1000))

**Defined in theory: Standard-units****Source code: standard-units.lisp**

English length unit.

**Axioms:**

(= Inch (/ Meter 39.37))

**Defined in theory: Standard-units****Source code: standard-units.lisp**

English length unit of feet.

**Axioms:**

(= Foot (* Inch 12))

**Defined in theory: Standard-units****Source code: standard-units.lisp**

English length unit.

**Axioms:**

(= Mile (* Foot 5280))

**Defined in theory: Standard-units****Source code: standard-units.lisp**

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)))

**Defined in theory: Standard-units****Source code: standard-units.lisp**

SI mass unit of kilogram.

**Instance-Of:**Si-unit, Unit-of-measure

**Axioms:**

(= (Quantity.Dimension Kilogram) Mass-Dimension)

**Defined in theory: Standard-units****Source code: standard-units.lisp**

English pound of mass.

**Axioms:**

(= Pound-Mass (/ Kilogram 2.2046))

**Defined in theory: Standard-units****Source code: standard-units.lisp**

English mass unit.

**Axioms:**

(= Slug (/ Pound-Mass 1000))

**Defined in theory: Standard-units****Source code: standard-units.lisp**

SI force unit.

**Axioms:**

(= Newton (* (* Kilogram Meter) (Expt Second-Of-Time -2)))

**Defined in theory: Standard-units****Source code: standard-units.lisp**

SI electrical current unit.

**Instance-Of:**Si-unit, Unit-of-measure

**Axioms:**

(= (Quantity.Dimension Ampere) Electrical-Current-Dimension)

**Defined in theory: Standard-units****Source code: standard-units.lisp**

English pound of force.

**Axioms:**

(= Pound-Force (/ Newton 4.448))

**Defined in theory: Standard-units****Source code: standard-units.lisp**

SI energy unit.

**Axioms:**

(= Joule (* Newton Meter))

**Defined in theory: Standard-units****Source code: standard-units.lisp**

British thermal unit, a unit of energy.

**Axioms:**

(= Btu (* 1055.0 Joule))

**Defined in theory: Standard-units****Source code: standard-units.lisp**

SI pressure unit.

**Axioms:**

(= Pascal (* Newton (Expt Meter -2)))

**Defined in theory: Standard-units****Source code: standard-units.lisp**

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)

**Defined in theory: Standard-units****Source code: standard-units.lisp**

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)))

**Defined in theory: Standard-units****Source code: standard-units.lisp**

Angular measurement unit.

**Axioms:**

(= Radian Identity-Unit)

**Defined in theory: Standard-units****Source code: standard-units.lisp**

Angular measurement unit.

**Axioms:**

(= Degree (* Radian (/ Pi 180)))

**Defined in theory: Standard-units****Source code: standard-units.lisp**

An example currency unit.

**Instance-Of:**Unit-of-measure

**Axioms:**

(= (Quantity.Dimension Us-Dollar) Currency-Dimension)

**Defined in theory: Standard-units****Source code: standard-units.lisp**

Currency measurement unit.

**Axioms:**

(= Us-Cent (/ Us-Dollar 100))

**Defined in theory: Standard-units****Source code: standard-units.lisp**

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)

**Defined in theory: Standard-units****Source code: standard-units.lisp**

The CANDELA is the SI unit for luminous intensity.

**Instance-Of:**Si-unit, Unit-of-measure

**Axioms:**

(= (Quantity.Dimension Candela) Luminous-Intensity-Dimension)

**Defined in theory: Standard-units****Source code: standard-units.lisp**

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