The most controversial condition that the AGM theory of rational belief change places on belief contraction is the recovery condition. The condition is controversial because of a series of putative counterexamples due (separately) to I. Levi and S. O. Hansson. In this paper we show that the conflicts that Levi and Hansson arrange between AGM contraction and our intuitions about how to give up beliefs are merely apparent. We argue that these conflicts disappear once we attend more closely to the (...) identification of the beliefs contracted away in each counterexample case. Since, on our view, speakers' belief contraction intentions are often more complicated than they may first appear, we are led to develop apparatus for thinking about the communication and identification of those intentions. Our argument refocuses attention on the difficult question of how to apply the AGM theory to particular cases. (shrink)

This paper continues the recent tradition of investigating iterated AGM revision by reasoning directly about the dynamics for total pre-order (“implausibility ordering”) representations of AGM revision functions. We reorient discussion, however, by proving that symmetry considerations, almost by themselves, suffice to determine a particular, AGM-friendly implausibility ordering dynamics due to Spohn 1988, which we call “J-revision”. After exploring the connections between implausibility ordering dynamics and the social choice theory of Arrow 1963, we provide symmetry arguments in the social choice-theoretic framework (...) for an interesting generalization of J-revision due to Nayak 1994. We conclude by arguing that the symmetry principles that uniquely favor J-revision and its generalizations are importantly expressive of the purely qualitative framework for representing beliefs that distinguishes the AGM program. Our results therefore comprehensively vindicate Spohn's 1988 conjecture that essentially J-revision is the best that can be done by way of a purely qualitative model of belief revision. (shrink)

If we suppose that reasonable belief is reasonable not because it has a foundation but because it is self-correcting, and that bodies of reasonable belief are self-correctable in virtue of their web-like internal structure, then it becomes natural to ask for explicit accounts both of self-correction itself, and of the web-like internal structure that makes self-correction possible: The theory of rational belief change. ;In this essay we study qualitative, logical theories of rational belief change, in particular the AGM account, and (...) its offshoot, the theory base account. Throughout, however, we use quantitative, probabilistic models as foils. ;We first undertake a systematic, critical study of the AGM account, focusing especially on its "possible worlds" formulation and on its theory of belief revision. According to the AGM account we can represent AGM revision by simple computations over total preorders of possibilities. We investigate iterated AGM revision from this perspective, and prove that symmetry considerations familiar from social choice theory essentially determine a particular ordering dynamics. These symmetry arguments put an upper bound on the sorts of responsiveness we can expect from the AGM model of rational belief change. The most widely criticized feature of the AGM account is its "recovery" condition on belief contraction. We show how to deflect all existing criticisms to recovery by paying close to attention to exactly which beliefs are given up in a particular case. The principal cost of this strategy is that the AGM account becomes harder to apply and to test. ;Theory base accounts add a layer of syntactically-encoded information to the AGM model. We show that this approach fails comprehensively: that it cannot successfully coordinate the syntactic layer of information with underlying contents or with necessary ordering information, and that it sanctions demonstrably irrational belief changes. Our diagnosis is, in part, that the theory base account conflates two distinct sorts of nonmonotonic belief change. ;Lastly, we summarize our current research into quantitative accounts of rational belief change, focusing on a model that generalizes irreducibly two-place probability, and that has the AGM account as a limiting case. (shrink)