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.

A number of studies that compare the effectiveness of data presented in graphic form versus data presented in tabular form have been performed. Results have been mixed. In a study by Dickson et al. (1986) that used business students as subjects it is suggested that task variables are paramount in the determination of such effectiveness. It is suggested that the type of data and type of subject used in the work by Dickson et al. favored tabular presentation and compromise any generalization of their conclusions. The current study finds that user training/expertise is a critical variable in determining the effectiveness of graphs versus tables. The conclusion drawn is that a user-friendly system should make both modes available so that the users have the option of selecting their preferred mode.>