Weaker Forms of Monotonicity for Declarative Networking

@article{Ameloot2016WeakerFO,
  title={Weaker Forms of Monotonicity for Declarative Networking},
  author={Tom J. Ameloot and Bas Ketsman and Frank Neven and Daniel Zinn},
  journal={ACM Transactions on Database Systems (TODS)},
  year={2016},
  volume={40},
  pages={1 - 45}
}
The CALM-conjecture, first stated by Hellerstein [2010] and proved in its revised form by Ameloot et al. [2013] within the framework of relational transducer networks, asserts that a query has a coordination-free execution strategy if and only if the query is monotone. Zinn et al. [2012] extended the framework of relational transducer networks to allow for specific data distribution strategies and showed that the nonmonotone win-move query is coordination-free for domain-guided data… 

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Parallel-Correctness and Containment for Conjunctive Queries with Union and Negation
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It is shown that the containment problem for conjunctive queries with negation is coNEXPTIME-complete and the study of the complexity of parallel-correctness and its constituents, parallel-soundness and parallel-completeness is extended.
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Weaker Forms of Monotonicity for Declarative Networking: A More Fine-Grained Answer to the CALM-Conjecture
TLDR
Equating increasingly larger classes of coordination-free computations with increasingly weaker forms of monotonicity and present explicit Datalog variants that capture each of these classes can be interpreted as a more fine-grained answer to the CALM-conjecture.
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