A important form of consistency is Read-Your-Write. Here, it is guaranteed that after a process updates the value of X to, say, b, all subsequent reads from that process will read b.
An important practical variation of this is session consistency—here, all access happens in the context of a session. For a valid session, the system guarantees Read-Your-Write semantics for any process. However, when the session is expired or deleted, there is no ordering guaranteed.