Weak Forms of Monotonicity and Coordination-Freeness
  Our earlier work titled: "Win-move is Coordination-Free (Sometimes)" has shown that the classes of queries that can be distributedly computed in a coordination-free manner form a strict hierarchy depending on the assumptions of the model for distributed computations. In this paper, we further characterize these classes by revealing a tight relationship between them and novel weakened forms of monotonicity. 
Daniel Zinn
cs.DB cs.DC