# Class SYSTEM-OF-UNITS

## Slots on this class:

Documentation:
A system-of-units is a class of units of measure that defines a standard system of measurement. Each instance of the class is a canonical unit-of-measure for a dimension. The mapping from dimensions to units in the system is provided by the function called standard-unit; since this mapping is functional and total, there is exactly one unit in the system of units per dimension.

There is no intrinsic property of a dimension that makes it fundamental or primitive, and neither is there any such property for units of measure. However, each system of units is defined by a basis set of units, from which all other units in the system are composed. The function base-units maps a system-of-units to its basis set. The dimensions of the units in the base-set must be orthogonal (see the definition of fundamental-dimension-set). For each composition of these fundamental dimensions (e.g., length / time) there is a corresponding unique unit in the system-of-units (e.g., meter / second-of-time).

The System International (SI) standard used in physics is a system-of-units based on seven fundamental dimensions and base units. Other systems of units may have different basis sets of differing cardinality, yet share some of the same units as the SI system.

Subclass-Of: Class

## Slots on instances of this class:

Subclass-Of: Unit-of-measure
Base-Units:
Slot-Cardinality: 1

## Axioms:

```(<=> (System-Of-Units ?System)
(And (Class ?System)
(Subclass-Of ?System Unit-Of-Measure)
(=> (Instance-Of ?Unit ?System)
(= (Standard-Unit ?System (Quantity.Dimension ?Unit))
?Unit))
(Value-Cardinality ?System Base-Units 1)
(=> (Member ?Unit (Base-Units ?System))
(Instance-Of ?Unit ?System))
(Orthogonal-Dimension-Set
(Setofall ?Dim
(Exists (?Unit)
(And (Member ?Unit
(Base-Units ?System))
(= ?Dim
(Quantity.Dimension ?Unit))))))))

```

## Notes:

• Example: (system-of-units si-unit)

• ((can any set of units be the base-set for a system of units? no, the base-units in a system of units must not be compositions
of each other. for example, if the base units included meter, second-of-time, and (unit* meter second-of-time), then it would not be a system of units, because the dimension of (unit* meter second-of-time) is (* length-dimension
time-dimension), which is a composition of other ``fundamental'' dimensions.))