A scalar-quantity is a constant quantity whose magnitude is a real number. An important property of scalar-quantities is that they form a field with respect to the addition and multiplication (with proper subclass restrictions). The class of scalar-quantities forms a partial order with the less-than relation <, since < is a relation-extended-to-quantities and < is defined over the reals. The < relation is not a total order over the class of scalar-quantity
since elements from some subclasses such as length quantities are incomparable to elements from other subclasses such as mass quantities.
(<=> (Scalar-Quantity ?Q)
(And (Constant-Quantity ?Q)
(Forall (?U)
(=> (And (Unit-Of-Measure ?U)
(Compatible-Quantities ?U ?Q))
(Real-Number (Magnitude ?Q ?U))))))