A formal framework for the development of algebraic specifications is presented. Ther main issues concerning the approach are the following: we allow to deal with incomplete specifications during the design process. This is handled by means of loose semantics and initial constraints. The design process is considered bi-dimensional. Horizontal refinements express, as usual, extensions. Vertical refinements consists in adding more detail or completing the refined specifications. The usual composition properties for refinements hold in our framework. In addition, the horizontal composition theorem defines a generalization of parameter passing as it is usually understood.Postprint (published version
