Belief Liberation (and Retraction)
By Richard Booth, Samir Chopra, Aditya Ghose and Thomas Meyer
We provide a formal study of belief retraction operators that do not necessarily satisfy the (Inclusion) postulate. Our intuition is that a rational description of belief change must do justice to cases in which dropping a belief can lead to the inclusion, or 'liberation', of others in an agent's corpus. We provide a few possible weakenings of the (Inclusion) postulate and then provide two models of liberation via retraction operators, σ-liberation and linear liberation. We show that the class of σ-liberation operators is included in the class of linear ones and provide axiomatic characterisations for each class. We also show how any given retraction operator (including the liberation operators) can be 'converted' into either a withdrawal operator (i.e., satisfying (Inclusion)) or a revision operator via (a slight variant of) the Harper Identity and the Levi Identity respectively.