It is a convention, not a rule, in mathematics to use (+) to represent operations that are commutative (i.e. abelian) groups.
But this convention is not at all respected in programming (e.g. + for string concatenation in many languages) so I have to admit that it's pretty irrelevant.
A symbol's property depend on the operation, the multiplication symbol for example is commutative in some cases and not in others.