Resumo: In Computer Science, stepwise refinement of algebraic specifications is a well known formal methodology for rigorous program development. This talk illustrates how techniques from Algebraic Logic, in particular the notion of interpretation, understood as a multifunction that preserves and reflects logical consequence, captures a number of relevant transformations in the context of software design difficult to deal with in classical approaches. Examples include data encapsulation and the decomposition of operations into atomic transactions. But if interpretations open such a new research avenue in program refinement, (conceptual) tools are needed to reason about them. Therefore, we will also discuss a correspondence between logical interpretations and morphisms for a particular kind of coalgebras, so that usual coalgebraic constructions, such as bisimulation, can be used to reason about interpretations between (abstract) logics.