Slots on this class:
- Documentation:
A set of orthogonal dimensions; i.e., dimensions that cannot be
composed from each other.
- Instance-Of: Class
- Subclass-Of: Simple-set
- Has-Instance:
(Setofall ?Dim
(Exists (?Unit)
(And (Member ?Unit (Base-Units ?System))
(= ?Dim (Quantity.Dimension ?Unit)))))
Implication Axioms:
(=> (Member ?Dim ?Set-Of-Dimensions)
(And (Physical-Dimension ?Dim)
(Not (Dimension-Composable-From ?Dim
(Difference
?Set-Of-Dimensions
(Setof ?Dim))))))
Equivalence Axioms:
(<=> (Orthogonal-Dimension-Set ?Set-Of-Dimensions)
(And (Simple-Set ?Set-Of-Dimensions)
(=> (Member ?Dim ?Set-Of-Dimensions)
(And (Physical-Dimension ?Dim)
(Not (Dimension-Composable-From
?Dim
(Difference ?Set-Of-Dimensions
(Setof ?Dim))))))))
Axioms:
(Simple-Set ?Set-Of-Dimensions)
Other Related 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))))))))
(<=> (Orthogonal-Dimension-Set ?Set-Of-Dimensions)
(And (Simple-Set ?Set-Of-Dimensions)
(=> (Member ?Dim ?Set-Of-Dimensions)
(And (Physical-Dimension ?Dim)
(Not (Dimension-Composable-From
?Dim
(Difference ?Set-Of-Dimensions
(Setof ?Dim))))))))