Relevance, recovery and recuperation: A prelude to ring withdrawal

Abstract

In this paper, we introduce recuperative withdrawals, belief change operators that satisfy recuperation, a postulate weaker than recovery, all the AGM postulates for contraction except recovery and another postulate which is a slightly stronger condition than conjunctive inclusion. Furthermore, we present a constructive definition for a class of operators —named ring withdrawals— which are such that the outcome of a ring withdrawal of a belief set K by a sentence α is obtained by adding to the set of most plausible models ‖K‖ all the worlds which are as close to ‖K‖ as its closest ¬α-worlds. Ring withdrawals satisfy the Lindström and Rabinowicz's interpolation thesis. We show that the classes of recuperative withdrawals and of ring withdrawals are identical. Additionally we show that the class of ring withdrawals is not contained in and does not contain the class of AGM contractions or the class of severe withdrawals. Finally we present methods for defining an operator of ring withdrawal by means of a severe withdrawal operator and by means of an AGM contraction operator, and vice-versa.