Kinetic Consistency and Relevance in Belief Revision

A critical aspect of rational belief revision that has been neglected by the classical AGM framework is what we call the principle of kinetic consistency. Loosely speaking, this principle dictates that the revision policies employed by a rational agent at different belief sets, are not independent, but ought to be related in a certain way. We formalise kinetic consistency axiomatically and semantically, and we establish a representation result explicitly connecting the two. We then combine the postulates for kinetic consistency, with Parikh's postulate for relevant change, and add them to the classical AGM postulates for revision; we call this augmented set the extended AGM postulates. We prove the consistency and demonstrate the scope of the extended AGM postulates by showing that a whole new class of concrete revision operators introduced hererin, called PD operators, satisfies all extended AGM postulates. PD operators are of interest in their own right as they are natural generalisations of Dalal's revision operator. We conclude the paper with some examples illustrating the strength of the extended AGM postulates, even for iterated revision scenarios.