**Defined in theory: Scalar-quantities****Source code: scalar-quantities.lisp****Also defined in:**Kif-numbers, Physical-quantities, Unary-scalar-functions, Basic-matrix-algebra, Tensor-quantities

**Documentation:**+ defines the specialization of the quantity addition operator + for scalar-quantities. The operator enforces the restriction that the quantities be compatible. The operator is defined in terms of the number addition operator + and the magnitudes of quantities for a particular unit. Scalar-Quantities of a common dimension form an abelian group with respect to this operator and the zero-scalar of the same physical dimension.

(Forall (?D) (=> (Physical-Dimension ?D) (Abelian-Group (Scalar-Quantities-Of-Dimension ?D) + (The-Zero-Scalar-For-Dimension ?D)))) (=> (And (Scalar-Quantity ?X) (Scalar-Quantity ?Y)) (<=> (+ ?X ?Y ?Z) (And (Scalar-Quantity ?Z) (Forall (?U) (=> (And (Unit-Of-Measure ?U) (Compatible-Quantities ?X ?U)) (= (+ (Magnitude ?X ?U) (Magnitude ?Y ?U)) (Magnitude ?Z ?U)))))))