A survey of multiple contractions

@article{Fuhrmann1994ASO,
  title={A survey of multiple contractions},
  author={Andr{\'e} Fuhrmann and Sven Ove Hansson},
  journal={Journal of Logic, Language and Information},
  year={1994},
  volume={3},
  pages={39-75}
}
The AGM theory of belief contraction is extended tomultiple contraction, i.e. to contraction by a set of sentences rather than by a single sentence. There are two major variants: Inpackage contraction all the sentences must be removed from the belief set, whereas inchoice contraction it is sufficient that at least one of them is removed. Constructions of both types of multiple contraction are offered and axiomatically characterized. Neither package nor choice contraction can in general be… 
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Decomposition of multiple AGM contraction: possibility and impossibility results
TLDR
It is concluded that multiple contraction adds to the expressive power of belief revision theory and highlights the importance of studying multiple belief change, and multiple conclusion logic in general.
Belief revision by sets of sentences
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    Journal of Computer Science and Technology
  • 2008
The aim of this paper is to extend the system of belief revision developed by Alchourrón, Gärdenfors and Makinson (AGM) to a more general framework. This extension enables a treatment of revision not…
Belief revision by sets of sentences
The aim of this paper is to extend the system of belief revision developed by Alchourron, Gardenfors and Makinson (AGM) to a more general framework. This extension enables a treatment of revision not…
Multiple Kernel Contraction
TLDR
This paper focuses on the extension of AGM that allows change for a belief base by a set of sentences instead of a single sentence, and proposes for their model another way to construct functions: Multiple Kernel Contraction, that is a modification of kernel Contraction proposed by Hansson.
Multiple contraction revisited
Multiple contraction consists in giving up several beliefs at once. The treatments of multiple contraction in AGM belief revision theory have remained unsatisfactory. The paper proposes a clear,…
Maximal and perimaximal contraction
TLDR
It is shown that partial meet contraction is exactly characterized by adding to one of these constructions the condition that all logically closed subsets of the belief set can be obtained as the outcome of a single (multiple) contraction.
Possible Worlds Semantics for Partial Meet Multiple Contraction
TLDR
This paper presents the possible worlds semantics for partial meet multiple contractions and generalized Partial Meet Contraction to the case of contractions by (possibly non-singleton) sets of sentences.
Residual Contraction
TLDR
The class of partial meet contractions is a strict subclass of the class of residual contractions, a new kind of contraction operators for belief bases, and an extra condition is identified that may be added to the definition of residualcontractions.
Multiple and iterated contraction reduced to single-step single-sentence contraction
TLDR
Two ways to reduce finitely multiple contraction to contraction by single sentences are introduced and it is shown how iterated contraction can be reduced to single-step, single- sentence contraction.
Coherentist Contraction
TLDR
A model of coherentist belief contraction is constructed and the contraction operators obtained are shown to coincide with well-known belief base operations, indicating a connection between coherentist and “foundationalist” approaches to belief change.
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References

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