Belief revision conditionals: basic iterated systems

Annals of Pure and Applied Logic 96 (1-3):3-28 (1999)

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Abstract
It is now well known that, on pain of triviality, the probability of a conditional cannot be identified with the corresponding conditional probability [25]. This surprising impossibility result has a qualitative counterpart. In fact, Peter Gärdenfors showed in [13] that believing ‘If A then B’ cannot be equated with the act of believing B on the supposition that A — as long as supposing obeys minimal Bayesian constraints. Recent work has shown that in spite of these negative results, the question ‘how to accept a conditional?’ has a clear answer. Even if conditionals are not truth-carriers, they do have precise acceptability conditions. Nevertheless most epistemic models of conditionals do not provide acceptance conditions for iterated conditionals. One of the main goals of this essay is to provide a comprehensive account of the notion of epistemic conditionality covering all forms of iteration. First we propose an account of the basic idea of epistemic conditionality, by studying the conditionals validated by epistemic models where iteration is permitted but not constrained by special axioms. Our modeling does not presuppose that epistemic states should be represented by belief sets (we only assume that to each epistemic state corresponds an associated belief state). A full encoding of the basic epistemic conditionals (encompassing all forms of iteration) is presented and a representation result is proved. In the second part of the essay we argue that the notion of change involved in the evaluation of conditionals is suppositional, and that such notion should be distinguished from the notion of updating (modelled by AGM and other methods). We conclude by considering how some of the recent modellings of iterated change fare as methods for iterated supposing
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DOI 10.1016/s0168-0072(98)00028-1
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References found in this work BETA

A Counterexample to Modus Ponens.Vann McGee - 1985 - Journal of Philosophy 82 (9):462-471.
On the Logic of Iterated Belief Revision.Adnan Darwiche & Judea Pearl - 1997 - Artificial Intelligence 89:1-29.
Two Recent Theories of Conditionals.Allan Gibbard - 1981 - In William Harper, Robert C. Stalnaker & Glenn Pearce (eds.), Ifs. Reidel. pp. 211-247.

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Citations of this work BETA

Embedding If and Only If.Adam Sennet & Jonathan Weisberg - 2012 - Journal of Philosophical Logic 41 (2):449-460.
Conditionals in Reasoning.John Cantwell - 2009 - Synthese 171 (1):47 - 75.
Lewis’ Triviality for Quasi Probabilities.Eric Raidl - forthcoming - Journal of Logic, Language and Information:1-35.
Iterative Probability Kinematics.Horacio Arló-Costa & Richmond Thomason - 2001 - Journal of Philosophical Logic 30 (5):479-524.
The Logic of Dominance Reasoning.John Cantwell - 2006 - Journal of Philosophical Logic 35 (1):41-63.

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Iterated Revision and Minimal Change of Conditional Beliefs.Craig Boutilier - 1996 - Journal of Philosophical Logic 25 (3):263 - 305.
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On the Logic of Iterated Belief Revision.Adnan Darwiche & Judea Pearl - 1997 - Artificial Intelligence 89:1-29.
Iterative Probability Kinematics.Horacio Arló-Costa & Richmond Thomason - 2001 - Journal of Philosophical Logic 30 (5):479-524.

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