Revision by Conditionals: From Hook to Arrow

TL;DR

This paper introduces a flexible method to extend belief revision operators to handle conditionals, using a 'plug and play' approach that relates conditional revision to factual revision, advancing the theoretical understanding of belief updates.

Contribution

It proposes a novel, abstract method for extending belief revision operators to conditionals, independent of specific factual revision strategies.

Findings

Defines a 'plug and play' extension method for conditionals

Ensures the extension satisfies new, independent constraints

Relates conditional revision to factual revision via Ramsey Test

Abstract

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.