An Implementation of Belief Revision in Simplicial Models for Dynamic Epistemic Logic
Date:
In this talk we set out to show how to connect belief revision to dynamic epistemic logic by leveraging tools given by the setting of simplicial semantics. We start by modifying some of the existing models for DEL in simplicial semantics (“Knowledge and Simplicial Complexes”, “A Simplicial Complex Model for Dynamic Epistemic Logic”). In particular, we will show how to modify these models for DEL so that they work in a setting for belief, rather than knowledge, using tools from the upcoming paper “Belief In Simplicial Complexes”. With this in hand, we will then motivate an endogenous notion of “nearness” between facets, where two facets sharing more perspectives in common is interpreted as the two facets being more similar. We exploit this notion of “nearness” to give a model for belief revision ala Lewis’ “Probabilities of Conditionals and Conditional Probabilities”, and ultimately we use this notion of nearness to give a model of DEL where agents update via revision, rather than classically. We will conclude with a discussion of some existing and future work which attempts to exploit this notion of nearness to give new tools for fault tolerance.