On Iterated Contraction: Syntactic Characterization, Representation Theorem and Limitations of the Levi Identity

In this paper we study iterated contraction in the epistemic state framework, offering a counterpart of the work of Darwiche and Pearl for iterated revision. We provide pure syntactical postulates for iterated contraction, that is, the postulates are expressed only in terms of the contraction operator. We establish a representation theorem for these operators. Our results allow to highlight the relationships between iterated contraction and iterated revision. In particular we show that iterated revision operators form a larger class than that of iterated contraction operators. As a consequence of this, in the epistemic state framework, the Levi identity has limitations; namely, it doesn’t allow to define all iterated revision operators.

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