Simplicial Semantics for Belief Revision

If you've ever wondered why philosophers should care about simplicial semantics for modal logic, here is my answer! In this paper I show that simplicial semantics offers a nice implementation of belief revision à la Lewis. The basic idea is that, because simplicial semantics does not take worlds as foundational objects, worlds themselves have more "structure" that we can exploit. In particular, worlds are made up of "local states" of individual agents, and worlds sharing a particular agent's local state is how we model an agent being "uncertain" between the two worlds.

Building on the work here, the insight in this new paper was to use these local states also to model "nearness"; if two worlds share more local states, we say that they are nearer or more similar! This makes sense for the following reason: Worlds are composed of local states, hence having more local states in common makes two worlds more similar. The implementation of revision hence leverages a kind of "trust" between the agents. Agents revise to worlds that preserve as many of their fellow agents' local states as possible. This paper explores the philosophical dimensions of this, as well as proposes new directions one could take this work on this basis.

Recommended citation: Philip Sink (2026). "Simplicial Semantics for Belief Revision" arXiv
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