Abstract
In ‘belief revision’ a theory \( \mathcal{K} \) is revised with a formula ϕ resulting in a revised theory \( \mathcal{K}*\phi \). Typically, ¬ϕ is in \( \mathcal{K} \), one has to give up belief in ¬ϕ by a process of retraction, and ϕ is in \( \mathcal{K}*\phi \). We propose to model belief revision in a dynamic epistemic logic. In this setting, we typically have an information state (pointed Kripke model) for the theory \( \mathcal{K} \) wherein the agent believes the negation of the revision formula, i.e., wherein B¬ϕ is true. The revision with ϕ is a program *ϕ that transforms this information state into a new information state. The transformation is described by a dynamic modal operator [*ϕ], that is interpreted as a binary relation 〚*ϕ〛 between information states. The next information state is computed from the current information state and the belief revision formula. If the revision is successful, the agent believes ϕ in the resulting state, i.e., B ϕ is then true. To make this work, as information states we propose ‘doxastic epistemic models’ that represent both knowledge and degrees of belief. These are multi-modal and multi-agent Kripke models. They are constructed from preference relations for agents, and they satisfy various characterizable multi-agent frame properties. Iterated, revocable, and higher-order belief revision are all quite natural in this setting. We present, for an example, five different ways of such dynamic belief revision. One can also see that as a non-deterministic epistemic action with two alternatives, where one is preferred over the other, and there is a natural generalization to general epistemic actions with preferences.
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van Ditmarsch, H.P. (2005). Prolegomena to Dynamic Logic for Belief Revision. In: Uncertainty, Rationality, and Agency. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4631-6_7
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