Revision by Conditionals: From Hook to Arrow
This addresses a neglected issue in belief revision for AI and logic, providing a flexible approach that abstracts from controversial details, though it is incremental in extending existing operators.
The paper tackles the problem of extending belief revision operators to handle conditional inputs, introducing a 'plug and play' method that uniquely extends any iterated belief revision operator to the conditional case by linking it to revisions by material conditionals.
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 might one extend a revision operator to handle conditionals as input? Our approach to this question of 'conditional revision' is distinctive insofar as it abstracts from the controversial details of how to revise by factual sentences. 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.