Studia Logica 63 (1):49-84 (1999)

John Cantwell
Royal Institute of Technology, Stockholm
The problems that surround iterated contractions and expansions of beliefs are approached by studying hypertheories, a generalisation of Adam Grove's notion of systems of spheres. By using a language with dynamic and doxastic operators different ideas about the basic nature of belief change are axiomatised. It is shown that by imposing quite natural constraints on how hypertheories may change, the basic logics for belief change can be strengthened considerably to bring one closer to a theory of iterated belief change. It is then argued that the logic of expansion, in particular, cannot without loss of generality be strengthened any further to allow for a full logic of iterated belief change. To remedy this situation a notion of directed expansion is introduced that allows for a full logic of iterated belief change. The new operation is given an axiomatisation that is complete for linear hypertheories.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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Reprint years 2004
DOI 10.1023/A:1005219504371
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Severe Withdrawal (and Recovery).Hans Rott & Maurice Pagnucco - 1999 - Journal of Philosophical Logic 28 (5):501-547.
Iterated Belief Change and the Recovery Axiom.Samir Chopra, Aditya Ghose, Thomas Meyer & Ka-Shu Wong - 2008 - Journal of Philosophical Logic 37 (5):501-520.

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