Belief Change is one of the central research topics in Knowledge Representation and theory revision and contraction are two of the most important operators in Belief Change. Recently the original axiomatization of revision and contraction was extended to include epistemic input represented by a (possibly infinite) set of sentences (as opposed to a single sentence) giving rise to the operators of set revision (also known as multiple revision) and set contraction. Both set revision and set contraction have been characterized in terms of constructive models called system of spheres and epistemic grasp respectively. Based on these links, in this paper we provide a characterization of set contraction in terms of system of spheres, and we identify the necessary and sufficient conditions under which the system-of-spheres model and the epistemic-grasp model give rise to the same set contraction.
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