How to keep on changing your mind, dynamically
Presented at the Logic, Rationality and Interaction, Beijing
Bonanno [Bon07a] presents a modal language LB for reasoning about information and changes of belief with a branching next-time semantics. We provide here a complete axiomatisation (Theorem 2) of the resulting logic. Bonanno also presents LB axioms for the AGM [AGM85] theory change postulates. The AGM postulates say little about iterated change. And they are 'static' in van Benthem's [Ben06] terminology, so not suited for representing the beliefs of introspective single agents or interacting groups of agents. The current paper develops Bonanno's logic to transcend these two features of the AGM postulates. Firstly we give LB axioms for various iterated belief revision constraints discussed by Boutilier [Bou96], Darwiche and Pearl [DP97], Nayak et al [NPP03] and others (Propositions 5--14). This was explicitly left open in [Bon07a]. Secondly we propose alternative axioms that exploit the temporal vocabulary of the logic to capture the 'dynamic' aspect of revision that is present in van Benthem's [Ben06] proposal.