15 March 2007, Logics for Dynamics of Information and Preferences - Special Working sessions, François Lepage (Universite de Montreal)

There are two very different ways to represent the dynamics of belief. One is the well known conditionalization: An agent whose belief function is represented by a probability function Pr(X) shifts to Pr(X ∧ A)/Pr(A) after discovering that A is the case. An other kind of dynamics is associated with the evaluation of a counterfactual: Pr(A > B) = Pr_A(B) where Pr_A is obtained from Pr by some minimal change to obtain Pr _A(A) = 1. This is Imaging as introduced by David Lewis.

After a characterization of Lewis imaging, we ask the question of the possibility of extending imaging to the general framework of conditional probability functions, i.e. of the possibility of defining - given that conditional probability function Pr(X, Γ) is the primitive notion - Pr(A > B,Γ) using imaging. We show that there is no simple and intuitive way to do so.

For more information, see http://staff.science.uva.nl/~oroy/Working_sessions/