Reversing the Levi identity

@article{Hansson1993ReversingTL,
  title={Reversing the Levi identity},
  author={Sven Ove Hansson},
  journal={Journal of Philosophical Logic},
  year={1993},
  volume={22},
  pages={637-669}
}
  • S. Hansson
  • Published 1 December 1993
  • Philosophy
  • Journal of Philosophical Logic
The AGM (Alchourrón-GÄrdenfors-Makinson) model of belief change is extended to cover changes on sets of beliefs that arenot closed under logical consequence (belief bases). Three major types of change operations, namely contraction, internal revision, and external revision are axiomatically characterized, and their interrelations are studied. In external revision, the Levi identity is reversed in the sense that onefirst adds the new belief to the belief base, and afterwards contracts its… 
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insightful comments on an earlier draft of this paper. I thank the referees for Erkenntnis who, apart from giving extended commen ts and suggestions, provided me with some hard-to-nd relevant
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References

SHOWING 1-10 OF 23 REFERENCES
Belief contraction without recovery
TLDR
This work replaces recovery with the seemingly much weaker postulate of core-retainment, which ensures that if x is excluded from K when p is contracted, then x plays some role for the fact that K implies p.
Foundational belief change
TLDR
It is shown that the theory contraction operation generated by Fuhrmann's minimal base contraction operation, even under quite strong restrictions, fails to satisfy the “supplementary postulates” of belief contraction.
A nonmonotonic conditional logic for belief revision. Part 1: Semantics and logic of simple conditionals
  • H. Rott
  • Philosophy
    The Logic of Theory Change
  • 1989
TLDR
Using Gardenfors's notion of epistemic entrenchment, the semantics of a logic is developed which explains the nonmonotonic nature of the consequence relation governing languages which contain conditionals, and how to deduce conditionals from premise sets without conditionals.
Knowledge, belief, and strategic interaction: The dynamics of belief systems: Foundations versus coherence theories
1. The PROBLEM OF belief revision In this article I want to discuss some philosophical problems one encounters when trying to model the dynamics of epistemic states. Apart from being of interest in
On the Logic of Theory Change: Partial Meet Contraction and Revision Functions
TLDR
The authors investigate "partial meet contraction functions", which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated, and basic properties of these functions are established.
Belief Revision: Reason maintenance and belief revision: Foundations versus coherence theories
Recent years have seen considerable work on two approaches to belief revision: the so-called foundations and coherence approaches. The foundations approach supposes that a rational agent derives its
On the status of the postulate of recovery in the logic of theory change
We discuss the rather special status of the postulate of "recovery" among the six basic postulates for theory contraction as formulated and studied by Alchourr6n, Gdirdenfors and the author. Our
The Raft and the Pyramid: Coherence versus Foundations in the Theory of Knowledge
Contemporary epistemology must choose between the solid security of the ancient foundationalist pyramid and the risky adventure of the new coherentist raft. Our main objective will be to understand,
The Dynamics of Belief Systems : Foundations vs . Coherence Theories
In this article I want to discuss some philosophical problems one encounters when trying to model the dynamics of epistemic states. Apart from being of interest in themselves, I believe that
Hierarchies of Regulations and their Logic
TLDR
The relations between derogation and delivery are investigated, showing that although the two processes appear and are generally assumed to be quite different from each other, nevertheless for finite inconsistent codes, the composite process of derogating and then selecting a remainder turns out to be equipowerful with delivery.
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