Authors
Richard Booth
Cardiff University
Jake Chandler
La Trobe University
Abstract
Recent work has considered the problem of extending to the case of iterated belief change the so-called `Harper Identity' (HI), which defines single-shot contraction in terms of single-shot revision. The present paper considers the prospects of providing a similar extension of the Levi Identity (LI), in which the direction of definition runs the other way. We restrict our attention here to the three classic iterated revision operators--natural, restrained and lexicographic, for which we provide here the first collective characterisation in the literature, under the appellation of `elementary' operators. We consider two prima facie plausible ways of extending (LI). The first proposal involves the use of the rational closure operator to offer a `reductive' account of iterated revision in terms of iterated contraction. The second, which doesn't commit to reductionism, was put forward some years ago by Nayak et al. We establish that, for elementary revision operators and under mild assumptions regarding contraction, Nayak's proposal is equivalent to a new set of postulates formalising the claim that contraction by ¬A should be considered to be a kind of `mild' revision by A. We then show that these, in turn, under slightly weaker assumptions, jointly amount to the conjunction of a pair of constraints on the extension of (HI) that were recently proposed in the literature. Finally, we consider the consequences of endorsing both suggestions and show that this would yield an identification of rational revision with natural revision. We close the paper by discussing the general prospects for defining iterated revision in terms of iterated contraction.
Keywords Levi Identity  Iterated revision  Iterated contraction  belief revision  AGM  rational closure
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References found in this work BETA

Two Modellings for Theory Change.Adam Grove - 1988 - Journal of Philosophical Logic 17 (2):157-170.
The Irreducibility of Iterated to Single Revision.Jake Chandler & Richard Booth - 2017 - Journal of Philosophical Logic 46 (4):405-418.
Iterated Revision and Minimal Change of Conditional Beliefs.Craig Boutilier - 1996 - Journal of Philosophical Logic 25 (3):263 - 305.
Shifting Priorities: Simple Representations for Twenty-Seven Iterated Theory Change Operators.Hans Rott - 2006 - In David Makinson, Jacek Malinowski & Heinrich Wansing (eds.), Towards Mathematical Philosophy. Dordrecht: Springer. pp. 269–296.
Irrevocable Belief Revision in Dynamic Doxastic Logic.Krister Segerberg - 1998 - Notre Dame Journal of Formal Logic 39 (3):287-306.

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