The primary purpose of this paper is to shed light on the structure of four varieties of normative theories of supposition by systematically explicating the relationships between canonical representatives of each. These include qualitative and quantitative theories of indicative and subjunctive supposition. We approach this project by treating supposition as a form of 'provisional belief revision' in which a person temporarily accepts the supposition as true and makes some appropriate changes to her other opinions so as to accommodate their supposition. The idea is that suppositional judgments are supposed to reflect an agent's judgments about how things would be in some hypothetical state of affairs satisfying the supposition. Accordingly, our representative qualitative theories of indicative and subjunctive supposition are respectively based on AGM revision and KM update, while our representative quantitative ones are provided by conditionalization and imaging. We rely on a suitably adapted version of the Lockean thesis to generate qualitative judgments based on our representative quantitative theories. Ultimately, a number of new results are established that vindicate the often repeated claim that conditionalization is a probabilistic version of revision, while imaging is a probabilistic version of update
