This paper presents a refinement calculus for object systems with visibility, dynamic binding and mutual dependency. The intention is to support effective use of a relational model for specifying and reasoning in activities of an object system development process. The semantics framework will define the meaning of the combinators in the exactly same way as their counterparts in the imperative programming languages. This makes the approach more accessible to the users who are already familiar with the algebraic laws and the verification tools developed for these languages. The paper also provides aset of transformation rules in support of object system refinement.