I show that there is a common order-theoretic structure underlying many of the models for representing beliefs in the literature. After identifying this structure, and studying it in some detail, I show that it is useful: it can be used to generalise the coherentist study of belief dynamics (belief expansion and revision) by using an abstract order-theoretic definition of the belief spaces where the dynamics of expansion and revision takes place. Interestingly, many of the existing results for expansion and revision in the context of classical propositional logic can be proven in this much more abstract setting, and therefore remain valid for many other belief models, such as imprecise probability models.
Keywords. Belief model, belief revision, classical propositional logic, impreciseprobability, order theory, possibility measure, system of spheres.
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