A Conditional Perspective for Iterated Belief Contraction

According to Boutillier, Darwiche and Pearl and others, principles for iterated revision can be characterised in terms of changing beliefs about conditionals. For iterated contraction a similar formulation is not known. This is especially because for iterated belief change the connection between revision and contraction via the Levi and Harper identity is not straightforward, and therefore, characterisation results do not transfer easily between iterated revision and contraction. In this article, we develop an axiomatisation of iterated contraction in terms of changing conditional beliefs. We prove that the new set of postulates conforms semantically to the class of operators like the ones given by Konieczny and Pino Pérez for iterated contraction. 1 Introduction For the three main classes of theory change, revision, expansion and contraction, different characterisations are known [12], which are heavily supported by the correspondence between revision and contraction via the Levi and Harper identities [13, 17].