Belief contraction in the context of the general theory of rational choice

Hans Rott

pp. 269-302

in: Horacio Arló-Costa, Vincent F. Hendricks, Johan van Benthem (eds), Readings in formal epistemology, Berlin, Springer, 2016

Abstract

This paper reorganizes and further develops the theory of partial meet contraction which was introduced in a classic paper by Alchourrón, Gärdenfors and Makinson. Our purpose is threefold. First, we put it in a broader perspective by decomposing it into two layers which can respectively be treated by the general theory of choice and preference and elementary model theory. Second, we reprove the two main representation theorems of AGM and present two more representation results for the finite case that "lie between" the former, thereby partially answering an open question of AGM. Our method of proof is uniform insofar as it uses only one form of "revealed preference", and it explains where and why the finiteness assumption is needed. Third, as an application, we explore the logic characterizing theory contractions in the finite case which are governed by the structure of simple and prioritized belief bases.