Reasoning about the correctness of concurrent objects on weak memory models supported by modern multicore architectures is complicated. Traditional notions such as linearizability do not directly apply as the effect of an operation can become visible after the operation call has returned.

In this paper we develop a theory for correctness of concurrent objects under weak memory models. Central to our definitions is the concept of observations which determine when effects of operations become visible, and hence determine the semantics of objects, under a given memory model. The resulting notion of correctness, called object refinement, is generic as it is parameterised by the memory model under consideration. Our theory enforces the minimal constraints on the placing of observations and on the semantics of objects that underlie object refinement. Object refinement is suitable as a reference for correctness when proving new proof methods for objects under weak memory models to be sound and complete.