A Conditional Perspective for Iterated Belief Contraction
This work addresses a theoretical gap in belief change for AI and logic, but it is incremental as it extends known results to contraction.
The paper tackled the lack of a known axiomatization for iterated belief contraction in terms of conditional beliefs, unlike iterated revision, and developed a new set of postulates that semantically conform to existing operators.
According to Boutillier, Darwiche, 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.