Multiple and iterated contraction reduced to single-step single-sentence contraction

Hansson, Sven Ove

doi:10.1007/s11229-009-9688-4

Cited by 16 publications

(4 citation statements)

References 13 publications

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“…Arguments have been given why no two of the four contractions K ÷ p ÷ q, K ÷ q ÷ p, K ÷ {p, q}, and K ÷ ( p ∨ q) should be expected to coincide in general [100]. However, it has been argued that the order-dependence of iterated operations is in itself problematic since ideally we should treat the pieces of information that we receive on an equal footing, independently of the order in which they arrive [61,140].…”

Section: Multiple Changementioning

confidence: 99%

“…Most of the major AGM-related contraction operators have been generalized to multiple contraction: multiple partial meet contraction [100,119,173], multiple kernel contraction [89], multiple specified meet contraction [140], and a multiple version of Grove's sphere system [85,217]. Spohn has proposed a ranking-theoretic account of multiple package contraction [252].…”

Section: Multiple Changementioning

confidence: 99%

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AGM 25 Years

2011

Self Cite

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The 1985 paper by Carlos Alchourrón , Peter Gärdenfors, and David Makinson (AGM), "On the Logic of Theory Change: Partial Meet Contraction and Revision Functions" was the starting-point of a large and rapidly growing literature that employs formal models in the investigation of changes in belief states and databases. In this review, the first twentyfive years of this development are summarized. The topics covered include equivalent characterizations of AGM operations, extended representations of the belief states, change operators not included in the original framework, iterated change, applications of the model, its connections with other formal frameworks, computatibility of AGM operations, and criticism of the model.

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Section: Multiple Changementioning

confidence: 99%

Section: Multiple Changementioning

confidence: 99%

AGM 25 Years

2011

Self Cite

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“…That led, in particular, to the generalization of several of the existing models (of AGM contractions): The partial meet multiple contractions were presented in Hansson (1989) and Fuhrmann & Hansson (1994), the kernel multiple contractions were introduced in Fermé et al (2003), Hansson (2010) exposed the class of multiple specified meet contraction, Spohn (2010) proposed a ranking-theoretic account of multiple package contraction and, in Reis (2011) and , the class of system of spheres-based multiple contractions (which are a generalization of Grove's system of spheres-based (singleton) contractions) was introduced.…”

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confidence: 99%

Epistemic Entrenchment-Based Multiple Contractions

Fermé

Reis

2013

The Review of Symbolic Logic

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In this article we present a new class of multiple contraction functions-the epistemic entrenchment-based multiple contractions-which are a generalization of the epistemic entrenchment-based contractions (Gärdenfors, 1988;Gärdenfors & Makinson, 1988) to the case of contractions by (possibly nonsingleton) sets of sentences and provide an axiomatic characterization for that class of functions. Moreover, we show that the class of epistemic entrenchment-based multiple contractions coincides with the class of system of spheres-based multiple contractions introduced in Fermé & Reis (2012). §1. Introduction. The standard model of theory change was proposed by Alchourrón, Gärdenfors and Makinson in their seminal paper and is, nowadays, known as the AGM model. One of the main issues that is addressed by this model is the modeling of how information is removed from the set of beliefs of an agent, that is, the characterization of contraction functions. In that regard, in the mentioned paper, the class of partial meet contractions was introduced and axiomatically characterized. Subsequently, several constructive models have been presented in the literature for the class of contraction functions proposed in the AGM framework, such as the system of spheres-based contractions (Grove, 1988), safe/kernel contractions Hansson, 1994), and the epistemic entrenchment-based contractions (Gärdenfors, 1988;Gärdenfors & Makinson, 1988).In a posterior stage of the development of the theory of belief contraction, several researchers (e.g., Niederée, 1991;Hansson, 1989;Fuhrmann, 1991;Fuhrmann & Hansson, 1994) pointed out the need for defining operations that could account for the removal of sets with more than one element from a theory. In particular it was remarked in Fuhrmann & Hansson (1994) that a simple evidence of the usefulness and the necessity of the study of package contractions is the fact that, in general, a set which is intuitively acceptable as possible result of the package contraction of a theory K by a set of sentences, say {α, β}, is different from the set which results of: 1. contracting K by (the single sentence) α ∧ β, because to remove a conjunction it suffices to remove one of the conjuncts. 2. contracting K by α ∨ β, since, however the removal of a disjunction from a theory implies the removal of both disjuncts, the converse does not hold, that is, in order to remove the set {α, β} from K it is not necessary to remove the sentence α ∨ β from K (to see that this is so it is enough to consider the case when β = ¬α). 4613. first contracting by α and then (contracting the result of such contraction) by β, given that, on the one hand, the result of first contracting by α and then by β is not, in general, identical to that of first contracting by β and then by α, and, on the other hand, it is implicit in the notion of multiple contraction that, in such a process, all the sentences to be contracted are treated equally.In all that follows we will use the expression multiple contraction to refer to an operation of the above ...

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“…In comparison to iterated belief revision, the case of iterated belief contraction is less examined. Spohn [21], Hansson [10], Nayak et al [17,18], and [2] consider special aspects of iterated belief contraction, but to the best of our knowledge the recent paper by Konieczny and Pino Pérez [16] is the only work on propositional iterated contraction that addresses the general case. Similar to the work of Darwiche and Pearl, Konieczny and Pino Pérez adapt a set of AGM contraction postulates for the propositional case; these propositional contraction postulates where proposed by Caridroit, Konieczny and Marquis [3].…”

Section: Proposition 1 ([4])mentioning

confidence: 99%

Iterated contraction of propositions and conditionals under the principle of conditional preservation

Kern-Isberner¹,

Bock²,

Sauerwald³

et al.

EPiC Series in Computing

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Research on iterated belief change has focussed mostly on belief revision, only few papers have addressed iterated belief contraction. Most prominently, Darwiche and Pearl published seminal work on iterated belief revision the leading paradigm of which is the so-called principle of conditional preservation. In this paper, we use this principle in a thoroughly axiomatized form to develop iterated belief contraction operators for Spohn's ranking functions. We show that it allows for setting up constructive approaches to tackling the problem of how to contract a ranking function by a proposition or a conditional, respectively, and that semantic principles can also be derived from it for the purely qualitative case.

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Multiple and iterated contraction reduced to single-step single-sentence contraction

Cited by 16 publications

References 13 publications

AGM 25 Years

AGM 25 Years

Epistemic Entrenchment-Based Multiple Contractions

Iterated contraction of propositions and conditionals under the principle of conditional preservation

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