Function STANDARD-UNIT

• Defined in theory: Physical-quantities
• Source code: physical-quantities.lisp

Slots on this function:

Documentation:

The standard-unit for a given system and dimension is a unit in that system whose dimension is the given dimension.

Instance-Of: Function

Arity: 3

Equivalence Axioms:

(<=> (Standard-Unit ?System-Of-Units ?Dimension)
     (And (System-Of-Units ?System-Of-Units)
          (Physical-Dimension ?Dimension)
          (Unit-Of-Measure ?Unit)
          (Instance-Of ?Unit ?System-Of-Units)
          (= (Quantity.Dimension ?Unit) ?Dimension)))

Axioms:

(Nth-Domain Standard-Unit 3 Unit-Of-Measure)

(Nth-Domain Standard-Unit 2 Physical-Dimension)

(Nth-Domain Standard-Unit 1 System-Of-Units)

Other Related Axioms:

(=> (Instance-Of ?Unit ?System)
    (= (Standard-Unit ?System (Quantity.Dimension ?Unit)) ?Unit))

(<=> (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))))))))

(=> (= (Standard-Unit ?System-Of-Units ?Dimension) ?Unit)
    (= (Quantity.Dimension ?Unit) ?Dimension))

(=> (= (Standard-Unit ?System-Of-Units ?Dimension) ?Unit)
    (Instance-Of ?Unit ?System-Of-Units))

(=> (= (Standard-Unit ?System-Of-Units ?Dimension) ?Unit)
    (Unit-Of-Measure ?Unit))

(=> (= (Standard-Unit ?System-Of-Units ?Dimension) ?Unit)
    (Physical-Dimension ?Dimension))

(=> (= (Standard-Unit ?System-Of-Units ?Dimension) ?Unit)
    (System-Of-Units ?System-Of-Units))

(<- (Magnitude-In-System-Of-Units ?Q ?System)
    (Magnitude ?Q (Standard-Unit ?System (Quantity.Dimension ?Q))))