Great question. I'm kind of shooting in the dark on this one, but Bayesian inference does function as a probabilistic generalization of propositional logic, so

Great question. I'm kind of shooting in the dark on this one, but Bayesian inference does function as a probabilistic generalization of propositional logic, so in principle it seems like the framework should be able to accommodate at least some kind of scenarios involving logical statements. There are also lots of Bayesian language models. At the same time, there are impossibility theorems that show beliefs across a group cannot in general be aggregated in coherent ways. (Some of the counter examples look a lot like the one you give.) So the type of model we are introducing is necessarily only going to be able to apply to certain groups (and perhaps could help characterize collectively rational vs irrational groups). One other related comment: the case we have dealt with so far is mainly about how groups integrate new information (collective learning), not about the existing prior knowledge knowledge within the group.