>>neolef+K8
Unfortunately, not in a particularly clever way. CP systems such as MongoDB, HBase, etc. don't have this problem since each datum has an authoritative master. As you can imagine, this can result in some operational...unpleasantness due to the lack of liveness guarantees in the presence of a network partition.
Out of the well known open-source AP systems, Riak is probably the leader here since they implement well understood techniques from the literature such as CRDTs and vclocks.
EDIT: removed my statement about Cassandra since it was a bit misleading and jbellis answered above in greater detail.