how to restrict a superproperty to a subproperty

The definition of a property of a subclass as subproperty of a property of a superclass may require to exclude other interpretations of the said superproperty for instances of the subclass. This issue should clarify the way this constraint is expressed in FOL, in the scope note, or even in the superproperty declaration, and what other logical constraints such a declaration may imply.

A possible FOL version may be:

B(x)  ⇒ A(x) "subclass of"
pb(x,y)  ⇒ B(x)
pa(x,y)  ⇒ A(x)
pb(x,y)  ⇒ pa(x,y) "subproperty of"

B(x) ∧ pa(x,y)  ⇒  pb(x,y) "the restriction of pa for all instances of B"