Revision by Conditionals: From Hook to Arrow

The belief revision literature has largely focussed on the issue of how to revise one’s beliefs in the light of information regarding matters of fact. Here we turn to an important but comparatively neglected issue: How to model agents capable of acquiring information regarding which rules of inference (‘Ramsey Test conditionals’) they ought to use in reasoning about these facts. Our approach to this second question of so-called ‘conditional revision’ is distinctive insofar as it abstracts from the controversial details of how the address the first. We introduce a ‘plug and play’ method for uniquely extending any iterated belief revision operator to the conditional case. The flexibility of our approach is achieved by having the result of a conditional revision by a Ramsey Test conditional (‘arrow’) determined by that of a plain revision by its corresponding material conditional (‘hook’). It is shown to satisfy a number of new constraints that are of independent interest.