Taking Levi Identity Seriously: A Plea for Iterated Belief Contraction

Nayak, Abhaya C.; Goebel, Randy; Orgun, Mehmet A.; Pham, Tam

doi:10.1007/11811220_26

Cited by 17 publications

(16 citation statements)

References 9 publications

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“…Indeed, Booth & Paris [32], for instance, establish, as a corollary of a further result, that the rational closure of a set of conditionals Γ corresponds to the flattest TPO that satisfies it. 12 Similar results can be found in Rott [33], in relation to his E-minimal entailment, and Pearl [34], in relation to his 1-entailment, notions that are essentially identical to rational closure (regarding rational closure's relation to 1-entailment, see [34]; regarding its relation to E-minimal entailment, see [35]).…”

Section: The Synchronous Teamqueue Combinatorsupporting

confidence: 68%

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From iterated revision to iterated contraction: Extending the Harper Identity

Booth

Chandler

2019

Artificial Intelligence

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The study of iterated belief change has principally focused on revision, with the other main operator of AGM belief change theory, namely contraction, receiving comparatively little attention. In this paper we show how principles of iterated revision can be carried over to iterated contraction by generalising a principle known as the 'Harper Identity'. The Harper Identity provides a recipe for defining the belief set resulting from contraction by a sentence A in terms of (i) the initial belief set and (ii) the belief set resulting from revision by ¬A. Here, we look at ways to similarly define the conditional belief set resulting from contraction by A. After noting that the most straightforward proposal of this kind leads to triviality, we characterise a promising family of alternative suggestions that avoid such a result. One member of that family, which involves the operation of rational closure, is noted to be particularly theoretically fruitful and normatively appealing.

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Section: The Synchronous Teamqueue Combinatorsupporting

confidence: 68%

“…In contrast, work on the parallel problem of iterated contraction-the problem of how to adjust that corpus in response to a sequence of successive retractionswas only initiated far more recently and remains comparatively underdeveloped [9,10,11,12,13,14,15].…”

Section: Introductionmentioning

confidence: 99%

From iterated revision to iterated contraction: Extending the Harper Identity

Booth

Chandler

2019

Artificial Intelligence

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“…Darwiche and Pearl have enriched the AGM theory with extra postulates to deal with iterated revision [10]. Meanwhile, several newer proposals appeared for iterated revision (see [25] for an overview), but only a few dealing with contraction [4,23,28]. Expansion is usually a very simple operation, and *Correspondence: renata@ime.usp.br 2 Department of Computer Science, University of São Paulo, Rua do Matõ, 1010 -Cidade Universitária, São Paulo 05508-090, Brazil Full list of author information is available at the end of the article when the new information is consistent with the existing knowledge base it can be seen as a special case of revision.…”

Section: Introductionmentioning

confidence: 99%

On the logic of theory change: iteration of expansion

Fermé

Wassermann

2018

J Braz Comput Soc

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Constructing models that allow for iterated changes is one of the most studied problems in the literature on belief change. However, up to now, iteration of expansion was only studied as a special case of consistent revision and, as far we know, there is no work in the literature that deals with expansions into inconsistency in a supraclassical framework. In this paper, we provide a semantics for iterated expansion, as well as its axiomatic characterization. We extend the model to two well-known families of iterated belief change (natural and lexicographic). Iteration of expansion can be combined with existent models of iteration of revision and contraction. Since we are able to accommodate different inconsistent belief states, iteration of expansion allows us to define new belief change functions that are currently only defined for belief bases: semi-revision, external revision, as well as consolidation.

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“…(I −2) has been implicitly endorsed by Nayak and his colleagues (Nayak et al 2006). Somewhat surprisingly, (I −4) does not appear to have yet been discussed in the literature.…”

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confidence: 98%

Transmission Failure, AGM Style

Chandler

2012

Erkenn

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This article provides a discussion of the principle of transmission of evidential support across entailment from the perspective of bfelief revision theory in the AGM tradition. After outlining and briefly defending a small number of basic principles of belief change, which include a number of belief contraction analogues of the Darwiche-Pearl postulates for iterated revision, a proposal is then made concerning the connection between evidential beliefs and belief change policies in rational agents. This proposal is found to be sufficient to establish the truth of a much-discussed intuition regarding transmission failure.

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Taking Levi Identity Seriously: A Plea for Iterated Belief Contraction

Cited by 17 publications

References 9 publications

From iterated revision to iterated contraction: Extending the Harper Identity

From iterated revision to iterated contraction: Extending the Harper Identity

On the logic of theory change: iteration of expansion

Transmission Failure, AGM Style

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