Simplicial Actions for Distributed Protocols

This paper is my first step in trying to answer the following question: "Why should anyone _other_ than philosophers care about belief revision?" As such, it extends work from my tech memo, published earlier this year. The advantage of the notion of revision from the previous chapter is that, in the setting of simplicial semantics, we get nearness/similarity "for free". There are plenty of applications for tools that help agents learn or at least deal with contradictory information (see Byzantine agreement, database work, etc.). But revision has never been a tool used to this end. I think this is because, in an actual applied setting, giving a preference relation on worlds, or saying which worlds are more or less near/similar is too abstract to actually be implemented with any consistency. So, there's something appealing about a notion of nearness with philosophical motivation that one gets "for free".

This paper attempts to bring all of these threads together. Simplicial Semantics started as a project in Distributed computing, and action models were already the canonical tool for describing protocols with that particular application in mind. So, in this paper, I build action models that can leverage the models my advisor and I built for belief in the first chapter, and the notion of nearness I give in the second chapter, to define distributed protocols where agents can handle contradictory information using revision! The tech memo develops a particular such protocol, with disaster relief as the intended setting of application. This paper instead develops the notion more broadly. I also give my 2 cents about the advantages of dynamic epistemic logic as a tool in distributed computing more generally, and speculate about new ways of leveraging topological information in simplicial models for analyzing task solvability in the future. This question furthermore becomes all richer when one is dealing with agents who can revise! The most exciting future project IMO involves simulating these models. Because we can implement revision so easily here, being able to simulate how agents learn and evolve would actually allow philosophers to start _testing_ the efficacy of revision, something that so far has to my knowledge not really been possible, for reasons similar as to why revision hasn't been picked up as a tool in more applied settings. Being able to simulate dynamic logic could open up a plethora of new questions not previously answerable. More to come on simulations soon!

Recommended citation: Philip Sink (2026). "Simplicial Actions for Distributed Protocols" arXiv
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