Booth, Richard; Chopra, Samir; Ghose, Aditya K.; and Meyer, Thomas, 2005, Belief Liberation (and Retraction), Studia Logica: an international journal for symbolic logic, 79, 47-72.
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 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 show how any 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.