A New Semantics for Belief Revision in Simplicial Complexes

This paper represents the sum total of the work I completed for the Internship in Topology and Modal Logic with NASA LaRC. In this paper, we set out to do two things. Firstly, we wanted to identify features of simplicial semantics that would be difficult or obscure to leverage in the setting of traditional relational semantics. Secondly, we wanted to tie our research as closely as possible to the intended application of radio networks in disaster relief settings. Fortunately, the same insight met both of these goals. Two facets in a simplicial model can be considered ``nearer'' or ``more similar'' if they share more local states, i.e., they have a larger intersection. We use this to implement belief revision in the setting of simplicial semantics, getting nearness ``for free''. We then use that, in conjunction with tools from dynamic epistemic logic, to define a new gossip protocol. Anticipating on the one hand that there will be a great deal of contradictory information in the network in the intended application, and that one can't ignore or isolate "faulty" agents, we used belief revision to allow agents to handle this network without crashing. here.

Recommended citation: Philip Sink and Alwyn Goodloe (2026). "A New Semantics for Belief Revision in Simplicial Complexes" NASA Technical Reports Server
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