  We introduce an interleaving operational semantics for describing the
client-observable behaviour of atomic transactions on distributed key-value
stores. Our semantics builds on abstract states comprising centralised, global
key-value stores and partial client views. We provide operational definitions
of consistency models for our key-value stores which are shown to be equivalent
to the well-known declarative definitions of consistency model for execution
graphs. We explore two immediate applications of our semantics: specific
protocols of geo-replicated databases (e.g. COPS) and partitioned databases
(e.g. Clock-SI) can be shown to be correct for a specific consistency model by
embedding them in our centralised semantics; programs can be directly shown to
have invariant properties such as robustness results against a weak consistency
model.
