A survey of multiple contractions

  title={A survey of multiple contractions},
  author={Andr{\'e} Fuhrmann and Sven Ove Hansson},
  journal={Journal of Logic, Language and Information},
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… 
Decomposition of multiple AGM contraction: possibility and impossibility results
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
  • Dongmo Zhang
  • Mathematics
    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
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
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
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
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
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
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.


Belief contraction without recovery
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.
Reversing the Levi identity
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
Modellings for Belief Change: Base Contraction, Multiple Contraction, and Epistemic Entrenchment
A distinction is drawn between the set of explicit beliefs of a reasoner, the “belief base”, and the beliefs that are merely implicit, which are governed exclusively by the structure of the belief base.
Relations between the logic of theory change and nonmonotonic logic
The purpose of this paper is to investigate the close relations between the logic of theory change (alias belief revision) on the one hand, and nonmonotonic logic on the other. The connection is most
Hierarchies of Regulations and their Logic
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.
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
Multiple-Conclusion Logic
This is a sustained study of multiple-conclusion logic, reworks the fundamental ideas of logic to take account of multiple conclusions, and investigates the connections between multiple - and single - conclusion calculi.
Relevant logics, modal logics and theory change
This thesis is a contribution to applied relevant logics. In Part One relevant logics are presented proof-theoretically and semantically. These logics are then extended to modal logics. Completeness
Similarity semantics and minimal changes of belief
Different similarity relations on sets are introduced, and their logical properties are investigated. Close relationships are shown to hold between similarity relations that are based on symmetrical
Multiple contraction. A further case against Gärdenfors' principle of recovery
  • R. Niederée
  • Mathematics, Computer Science
    The Logic of Theory Change
  • 1989