Worlds of Events: Deduction with Partial Knowledge about Causality

Seyed Hossein Haeri
(Universite catholique de Louvain, Belgium)
Peter Van Roy
(Universite catholique de Louvain, Belgium)
Carlos Baquero
(Universidade do Minho, Portugal)
Christopher Meiklejohn
(Universite catholique de Louvain, Belgium)

Interactions between internet users are mediated by their devices and the common support infrastructure in data centres. Keeping track of causality amongst actions that take place in this distributed system is key to provide a seamless interaction where effects follow causes. Tracking causality in large scale interactions is difficult due to the cost of keeping large quantities of metadata; even more challenging when dealing with resource-limited devices. In this paper, we focus on keeping partial knowledge on causality and address deduction from that knowledge.

We provide the first proof-theoretic causality modelling for distributed partial knowledge. We prove computability and consistency results. We also prove that the partial knowledge gives rise to a weaker model than classical causality. We provide rules for offline deduction about causality and refute some related folklore. We define two notions of forward and backward bisimilarity between devices, using which we prove two important results. Namely, no matter the order of addition/removal, two devices deduce similarly about causality so long as: (1) the same causal information is fed to both. (2) they start bisimilar and erase the same causal information. Thanks to our establishment of forward and backward bisimilarity, respectively, proofs of the latter two results work by simple induction on length.

In Massimo Bartoletti, Ludovic Henrio, Sophia Knight and Hugo Torres Vieira: Proceedings 9th Interaction and Concurrency Experience (ICE 2016), Heraklion, Greece, 8-9 June 2016, Electronic Proceedings in Theoretical Computer Science 223, pp. 113–127.
Published: 10th August 2016.

ArXived at: https://dx.doi.org/10.4204/EPTCS.223.8 bibtex PDF
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