Prolegomena to dynamic logic for belief revision

Abstract

In 'belief revision' a theory is revised with a formula φ resulting in a revised theory. Typically, ¬φ is in, one has to give up belief in ¬φ by a process of retraction, and φ is in. 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 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 ãεš*φãε 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. © Springer 2005.