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. In order to model the transitions between time slices, we will use action models. These too already have a history in distributed computing. 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.