A New Semantics for Belief Revision in Simplicial Complexes

In this paper we set out to develop a novel method for handling transient faults in gossip
protocols. In particular, we are interested in settings where a signal “P” can come across
the network, followed by a signal “¬P” at a later time. These signals could even come from
the same agent, and any agent is capable of failing as such. The main idea to handle such
a dramatically faulty setting is to use a technique from the philosophical literature called
“belief revision”. [31] This allows agents to update on information contrary to their beliefs
without resorting to probabilities. However, belief revision is often difficult to implement
in a practical setting. Therefore, we turn towards using simplicial semantics for epistemic
modal logic to represent each single time-slice of a protocol. Such models already have
a history of applications in distributed computing. [25] [36] [19] [26] [24] [22] [23] [29]
In order to model the transitions between time slices, we will use action models. These
too already have a history in distributed computing. [26] [19] [3] [34] [39] [15] We will
modify the application of action models to simplicial complexes in order to incorporate
belief revision. In so doing, we will be able to define a novel gossip protocol for handling
the prescribed fault scenario.