Yet More Modal Logics of Preference Change and Belief Revision

We contrast Bonanno’s ‘Belief Revision in a Temporal Framework’ [15] with preference change and belief revision from the perspective of dynamic epistemic logic (DEL). For that, we extend the logic of communication and change of [11] with relational substitutions [8] for preference change, and show that this does not alter its properties. Next we move to a more constrained context where belief and knowledge can be defined from preferences [29; 14; 5; 7], prove completeness of a very expressive logic of belief revision, and define a mechanism for updating belief revision models using a combination of action priority update [7] and preference substitution [8]. 1 Reconstructing AGM Style Belief Revision Bonanno’s paper offers a rational reconstruction of Alchourrón Gärdenfors Makinson style belief revision (AGM belief revision) [1] (see also [22] and [23]), in a framework where modalities B for single agent belief and I for being informed are mixed with a next time operator © and its inverse ©−1. Both the AGM framework and Bonanno’s reconstruction of it do not explicitly represent the triggers that cause belief change in the first place. Iφ expresses that the agent is informed that φ, but the communicative action that causes this change in information state is not represented. Also, φ is restricted to purely propositional formulas. Another limitation that Bonanno’s reconstruction shares with AGM is that it restricts attention to a single agent: changes of the beliefs of agents about the beliefs of other agents are not analyzed. In these respects [15] is close to Dynamic Doxastic Logic (DDL), as developed in [38; 39].